Question

A number is divisible by both $5$ and $12$. By which another number will that number be always divisible?

Answer 1

Given that a number is divisible by both $5$ and $12$.

We have to find another number by which the given number is always divisible.

We know that

Factors of $5$ are $1,5$

Factors of $12$ are $1,2,3,4,6,12$

Since $5$ and $12$ have no common factor other than $1$, therefore they are co-primes and we know that if a number is divisible by two co-primes, then it is also divisible by their product.

The product of $5$ and $12$ $=5\times 12=60$.

Thus the number is always divisible by $60$.

Therefore, if a number is divisible by both $5$ and $12$, it will be divisible by $60$.