A Number is Divisible By Both 5 and 12. By Which Other Number Will That Number Be Always Divisible?


Question: A number is divisible by both 5 and 12. By which other number will that number be always divisible?

We will use the definition of co-prime numbers to answer this question. Two numbers or integers are co-prime if their common factor is only 1. 

Answer: If a number is divisible by both 5 and 12 it will be divisible by 60.

If a number x is divisible by co-prime numbers a and b, then x will also be divisible by the product of a and b.

Explanation: 

5 and 12 are co-prime numbers because the highest common factor of 5 and 12 is 1

So, if a number is divisible by both 5 and 12, it will always be divisible by 5 × 12 which is 60.

Consider the number 120.

It is divisible by 5 and 12 and it is also divisible by the product of 5 and 12 which is 60.

You can check with any number, if it is divisible by 5 and 12, it will be divisible by 60.

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