Question

Determine the greatest $3$-digit number exactly divisible by $8,10$ and $12.$

Answer 1

The smallest number which is divisible by $8,10$ and $12$ is the LCM of these numbers.

Now,

$8=2^3$

$10=2^1\times 5^1$

$12=2^2\times 3^1$

LCM $=2^3\times 3^1\times 5^1$

$=120$

$120$ is the smallest number which is divisible by $8,10$ and $12$

any number which is divisible by $8,10$ and $12$ will be a multiple of $120$

So, the greatest 3-digit number divisible by $8,10$ and $12$ is $=120\times 8=960$