Question

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

Answer 1

Find LCM of given numbers

Multiple of $24=2\times 2\times 2\times 3$

Multiple of $15=3\times 5$

Multiple of $36=2\times 2\times 3\times 3=22\times 33$

LCM of $24,15,36$ $=2^3\times 3^2\times 5=360$

Now, divide the greatest 6-digit number by$360$

$\Rightarrow 999999/360=2777.775$ with remainder $279$

Now,

$\Rightarrow 999999-279=999720$

Hence, the greatest 6-digit number divisible by $24,15$ and $36$ is $999720$.