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Find the smallest number which when increase by 17 excatly divisible by both 520 and 468

Posted by Shrutika Magdum 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 5 months ago

The smallest number divisible by 520 and 468 = LCM(520,468)
Prime factors of 520 and 468 are :
520 = 2³ {tex}\times{/tex} 5 {tex}\times{/tex} 13
468 = 2 {tex}\times{/tex} 2 {tex}\times{/tex} 3 {tex}\times{/tex} 3 {tex}\times{/tex} 13
Hence LCM(520,468) = 2³ {tex}\times{/tex} 3²{tex}\times{/tex} 5 {tex}\times{/tex} 13 = 8 {tex}\times{/tex} 9{tex}\times{/tex}5{tex}\times{/tex}13 = 4680
Now the smallest number which when increased by 17 is exactly divisible by both 520 and 468.
=LCM(520,468)-17
=4680-17
=4663

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