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Find the greatest number of six …

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Find the greatest number of six digits exactly divisible by 18,24 and 36

Posted by Rushita Kodali 6 years, 6 months ago

Sia ? 6 years, 6 months ago

LCM of 18,24 and 36
18 = 2 {tex}\times{/tex} 3²
24 = 2³ {tex}\times{/tex} 3
36 = 2² {tex}\times{/tex} 3²
LCM (18,24,36) = 2³{tex}\times{/tex} 3² = 72

Hence if any number is divisible by 72 that will be divisible by 18,24 and 36 also.
Now the largest 6 digit number is 999999

On dividing 999999 by 72 we get

{tex}\;999999=13888\times72+\;63=999936+63{/tex}
Hence 999936 is the greatest 6 digit number divisible by 18,24 and 36.

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