{"id":90425,"date":"2025-06-01T10:28:21","date_gmt":"2025-06-01T10:28:21","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90425"},"modified":"2025-06-01T10:28:21","modified_gmt":"2025-06-01T10:28:21","slug":"the-least-integer-when-multiplied-by-2940-becomes-a-perfect-square-is","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-least-integer-when-multiplied-by-2940-becomes-a-perfect-square-is\/","title":{"rendered":"The least integer when multiplied by 2940 becomes a perfect square is"},"content":{"rendered":"

The least integer when multiplied by 2940 becomes a perfect square is<\/p>\n

[amp_mcq option1=”10″ option2=”15″ option3=”20″ option4=”35″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2019<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is B) 15.
\n<\/section>\n
\nTo find the least integer by which 2940 must be multiplied to make it a perfect square, we need to find the prime factorization of 2940.
\n2940 = 294 * 10
\n294 = 2 * 147 = 2 * 3 * 49 = 2 * 3 * 7^2
\n10 = 2 * 5
\nSo, 2940 = (2 * 3 * 7^2) * (2 * 5) = 2^2 * 3^1 * 5^1 * 7^2.
\nFor a number to be a perfect square, the exponents of all prime factors in its prime factorization must be even.
\nIn the prime factorization of 2940 (2^2 * 3^1 * 5^1 * 7^2), the exponents of the prime factors are 2 (for 2), 1 (for 3), 1 (for 5), and 2 (for 7).
\nThe exponents of 3 and 5 are odd. To make them even, we need to multiply 2940 by 3^1 and 5^1.
\nThe least integer needed to multiply is 3 * 5 = 15.
\nWhen multiplied by 15, the number becomes 2^2 * 3^1 * 5^1 * 7^2 * (3 * 5) = 2^2 * 3^2 * 5^2 * 7^2 = (2 * 3 * 5 * 7)^2. This is a perfect square.
\n<\/section>\n
\nA number is a perfect square if and only if all the exponents in its prime factorization are even. To find the least multiplier to make a number a perfect square, identify the prime factors with odd exponents and multiply the number by the product of these prime factors raised to the power needed to make their exponents even (which will always be 1 for each such prime factor).
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

The least integer when multiplied by 2940 becomes a perfect square is [amp_mcq option1=”10″ option2=”15″ option3=”20″ option4=”35″ correct=”option2″] This question was previously asked in UPSC CAPF – 2019 Download PDFAttempt Online The correct answer is B) 15. To find the least integer by which 2940 must be multiplied to make it a perfect square, we … <\/p>\n

Detailed SolutionThe least integer when multiplied by 2940 becomes a perfect square is<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1119,1102],"class_list":["post-90425","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1119","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nThe least integer when multiplied by 2940 becomes a perfect square is<\/title>\n<meta name=\"description\" content=\"The correct answer is B) 15. To find the least integer by which 2940 must be multiplied to make it a perfect square, we need to find the prime factorization of 2940. 2940 = 294 * 10 294 = 2 * 147 = 2 * 3 * 49 = 2 * 3 * 7^2 10 = 2 * 5 So, 2940 = (2 * 3 * 7^2) * (2 * 5) = 2^2 * 3^1 * 5^1 * 7^2. For a number to be a perfect square, the exponents of all prime factors in its prime factorization must be even. In the prime factorization of 2940 (2^2 * 3^1 * 5^1 * 7^2), the exponents of the prime factors are 2 (for 2), 1 (for 3), 1 (for 5), and 2 (for 7). The exponents of 3 and 5 are odd. To make them even, we need to multiply 2940 by 3^1 and 5^1. The least integer needed to multiply is 3 * 5 = 15. When multiplied by 15, the number becomes 2^2 * 3^1 * 5^1 * 7^2 * (3 * 5) = 2^2 * 3^2 * 5^2 * 7^2 = (2 * 3 * 5 * 7)^2. This is a perfect square.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-least-integer-when-multiplied-by-2940-becomes-a-perfect-square-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The least integer when multiplied by 2940 becomes a perfect square is\" \/>\n<meta property=\"og:description\" content=\"The correct answer is B) 15. To find the least integer by which 2940 must be multiplied to make it a perfect square, we need to find the prime factorization of 2940. 2940 = 294 * 10 294 = 2 * 147 = 2 * 3 * 49 = 2 * 3 * 7^2 10 = 2 * 5 So, 2940 = (2 * 3 * 7^2) * (2 * 5) = 2^2 * 3^1 * 5^1 * 7^2. For a number to be a perfect square, the exponents of all prime factors in its prime factorization must be even. In the prime factorization of 2940 (2^2 * 3^1 * 5^1 * 7^2), the exponents of the prime factors are 2 (for 2), 1 (for 3), 1 (for 5), and 2 (for 7). The exponents of 3 and 5 are odd. To make them even, we need to multiply 2940 by 3^1 and 5^1. The least integer needed to multiply is 3 * 5 = 15. When multiplied by 15, the number becomes 2^2 * 3^1 * 5^1 * 7^2 * (3 * 5) = 2^2 * 3^2 * 5^2 * 7^2 = (2 * 3 * 5 * 7)^2. This is a perfect square.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-least-integer-when-multiplied-by-2940-becomes-a-perfect-square-is\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:28:21+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The least integer when multiplied by 2940 becomes a perfect square is","description":"The correct answer is B) 15. To find the least integer by which 2940 must be multiplied to make it a perfect square, we need to find the prime factorization of 2940. 2940 = 294 * 10 294 = 2 * 147 = 2 * 3 * 49 = 2 * 3 * 7^2 10 = 2 * 5 So, 2940 = (2 * 3 * 7^2) * (2 * 5) = 2^2 * 3^1 * 5^1 * 7^2. For a number to be a perfect square, the exponents of all prime factors in its prime factorization must be even. In the prime factorization of 2940 (2^2 * 3^1 * 5^1 * 7^2), the exponents of the prime factors are 2 (for 2), 1 (for 3), 1 (for 5), and 2 (for 7). The exponents of 3 and 5 are odd. To make them even, we need to multiply 2940 by 3^1 and 5^1. The least integer needed to multiply is 3 * 5 = 15. When multiplied by 15, the number becomes 2^2 * 3^1 * 5^1 * 7^2 * (3 * 5) = 2^2 * 3^2 * 5^2 * 7^2 = (2 * 3 * 5 * 7)^2. This is a perfect square.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/the-least-integer-when-multiplied-by-2940-becomes-a-perfect-square-is\/","og_locale":"en_US","og_type":"article","og_title":"The least integer when multiplied by 2940 becomes a perfect square is","og_description":"The correct answer is B) 15. To find the least integer by which 2940 must be multiplied to make it a perfect square, we need to find the prime factorization of 2940. 2940 = 294 * 10 294 = 2 * 147 = 2 * 3 * 49 = 2 * 3 * 7^2 10 = 2 * 5 So, 2940 = (2 * 3 * 7^2) * (2 * 5) = 2^2 * 3^1 * 5^1 * 7^2. For a number to be a perfect square, the exponents of all prime factors in its prime factorization must be even. In the prime factorization of 2940 (2^2 * 3^1 * 5^1 * 7^2), the exponents of the prime factors are 2 (for 2), 1 (for 3), 1 (for 5), and 2 (for 7). The exponents of 3 and 5 are odd. To make them even, we need to multiply 2940 by 3^1 and 5^1. The least integer needed to multiply is 3 * 5 = 15. When multiplied by 15, the number becomes 2^2 * 3^1 * 5^1 * 7^2 * (3 * 5) = 2^2 * 3^2 * 5^2 * 7^2 = (2 * 3 * 5 * 7)^2. This is a perfect square.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-least-integer-when-multiplied-by-2940-becomes-a-perfect-square-is\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:28:21+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-least-integer-when-multiplied-by-2940-becomes-a-perfect-square-is\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-least-integer-when-multiplied-by-2940-becomes-a-perfect-square-is\/","name":"The least integer when multiplied by 2940 becomes a perfect square is","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:28:21+00:00","dateModified":"2025-06-01T10:28:21+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is B) 15. To find the least integer by which 2940 must be multiplied to make it a perfect square, we need to find the prime factorization of 2940. 2940 = 294 * 10 294 = 2 * 147 = 2 * 3 * 49 = 2 * 3 * 7^2 10 = 2 * 5 So, 2940 = (2 * 3 * 7^2) * (2 * 5) = 2^2 * 3^1 * 5^1 * 7^2. For a number to be a perfect square, the exponents of all prime factors in its prime factorization must be even. In the prime factorization of 2940 (2^2 * 3^1 * 5^1 * 7^2), the exponents of the prime factors are 2 (for 2), 1 (for 3), 1 (for 5), and 2 (for 7). The exponents of 3 and 5 are odd. To make them even, we need to multiply 2940 by 3^1 and 5^1. The least integer needed to multiply is 3 * 5 = 15. When multiplied by 15, the number becomes 2^2 * 3^1 * 5^1 * 7^2 * (3 * 5) = 2^2 * 3^2 * 5^2 * 7^2 = (2 * 3 * 5 * 7)^2. This is a perfect square.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-least-integer-when-multiplied-by-2940-becomes-a-perfect-square-is\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-least-integer-when-multiplied-by-2940-becomes-a-perfect-square-is\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-least-integer-when-multiplied-by-2940-becomes-a-perfect-square-is\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"The least integer when multiplied by 2940 becomes a perfect square is"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90425","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=90425"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90425\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90425"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90425"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90425"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}