{"id":617477,"date":"2023-06-20T11:50:44","date_gmt":"2023-06-20T06:20:44","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/state-true-or-false-it-is-possible-that-hcf-and-lcm-of-two-numbers-can-be-24-and-540-respectively\/"},"modified":"2025-06-26T15:37:44","modified_gmt":"2025-06-26T10:07:44","slug":"state-true-or-false-it-is-possible-that-hcf-and-lcm-of-two-numbers-can-be-24-and-540-respectively","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/state-true-or-falseit-is-possible-that-hcf-and-lcm-of-two-n\/","title":{"rendered":"State true or false.It is possible that HCF and LCM of two numbers can be 24 and 540 respectively?"},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"State true or false.It is possible that HCF and LCM of two numbers can be 24 and 540 respectively?","custom_permalink":"question\/mathematics\/state-true-or-falseit-is-possible-that-hcf-and-lcm-of-two-n\/"},"categories":[],"acf":{"question":"<p style=\"margin-top:0pt; margin-bottom:0pt\"><span>State true or false.<\/span><\/p><br><p style=\"margin-top:0pt; margin-bottom:0pt\"><span>It is possible that HCF and LCM of two numbers can be 24 and 540 respectively?<\/span><\/p><br><pstyle=\"margin-top:0pt;margin-bottom:0pt\"><spanstyle=\"-aw-import:ignore\"><p><\/p><pstyle=\"margin-top:0pt;margin-bottom:0pt\"><spanstyle=\"-aw-import:ignore\"><p><\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt\"><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt\">","options":[{"option":"<span>True<\/span>","correct":false},{"option":"<span>False<\/span><span>&nbsp;<\/span>","correct":true}],"solution":"<span>It is required to find whether that HCF and LCM of two numbers can be 24 and 540 are possible.<\/span><br><span>Fundamental Theorem of Arithmetic states every composite number can be expressed as a product of primes, and this factorization is unique except for the order in which the prime factors occur. <\/span><br><span>HCF of two numbers <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mo>=<\/m:mo><m:mn>24<\/m:mn><\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span>. <\/span><br><span>LCM of two numbers <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mo>=<\/m:mo><m:mn>540<\/m:mn><\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span>.<\/span><br><span>Always a multiple of HCF is LCM. In other words, HCF totally divides LCM. Now, <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mtable columnalign=\"left\">\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mfrac>\r\n      <m:mrow>\r\n       <m:mi>L<\/m:mi><m:mi>C<\/m:mi><m:mi>M<\/m:mi><m:mtext>&nbsp;of&nbsp;two&nbsp;numbers<\/m:mtext><\/m:mrow>\r\n      <m:mrow>\r\n       <m:mi>H<\/m:mi><m:mi>C<\/m:mi><m:mi>F<\/m:mi><m:mtext>&nbsp;of&nbsp;tw&nbsp;numbers<\/m:mtext><\/m:mrow>\r\n     <\/m:mfrac>\r\n     <m:mo>=<\/m:mo><m:mfrac>\r\n      <m:mrow>\r\n       <m:mn>540<\/m:mn><\/m:mrow>\r\n      <m:mrow>\r\n       <m:mn>24<\/m:mn><\/m:mrow>\r\n     <\/m:mfrac>\r\n     \r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mfrac>\r\n      <m:mrow>\r\n       <m:mn>45<\/m:mn><\/m:mrow>\r\n      <m:mn>2<\/m:mn>\r\n     <\/m:mfrac>\r\n     \r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n   <m:mtr>\r\n    <m:mtd>\r\n     <m:mo>\u21d2<\/m:mo><m:mn>22.5<\/m:mn><m:mo>\u2260<\/m:mo><m:mi>I<\/m:mi><m:mi>n<\/m:mi><m:mi>t<\/m:mi><m:mi>e<\/m:mi><m:mi>g<\/m:mi><m:mi>e<\/m:mi><m:mi>r<\/m:mi>\r\n    <\/m:mtd>\r\n   <\/m:mtr>\r\n  <\/m:mtable>\r\n  \r\n <\/m:semantics><\/math>&nbsp;<br><span>Hence, two numbers cannot have HCF and LCM as 24 and 540 respectively.<\/span><br><span>Therefore, the given statement is false.<\/span><br><span>Thus, option 2 is correct.<\/span><br><span>&nbsp;<\/span>","subject":"Mathematics"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>State true or false.It is possible that HCF and LCM of two numbers can be 24 and 540 respectively? 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