Question

Find the greatest number of 6 digits exactly divisible by 24, 15 and 36.

Answer 1

Given integers,

$24,15$ and $36$

Getting prime factorization

$24=2^3$

$15=3\times 5$

$36=2^2\times 3^2$

$LCM=2^3\times 3^2\times 5=360$

The greatest six digit number $=9,99,999$

The greatest six digit number exactly divisible by given numbers

$\Rightarrow 999999-$ Remainder when $9,99,999$ is divided by $LCM$

The greatest six digit number exactly divisible by given numbers $=999999-279\Rightarrow 9,99,720$

Hence, the greatest six digit number exactly divisible by $24,15$ and $36$ is $9,99,720.$