Question

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

Answer 1

Hint: We will use the concept of co prime in which the two numbers are said to be co prime if their common factor is only 1 and divisibility here in order to solve the question. After that we will use the concept of the product to solve the question further.

Complete step-by-step solution -
Before solving the question we will first understand the term co-prime. The two numbers are said to be co prime if their common factor is only 1. For example if we consider the numbers 31 and 2 then we can clearly see that the only common number between these two is 1.
Also, we will consider the divisibility here. The two numbers 31 and 2 will have their product as 62. Now we will divide 62 by 31 and we will get 2 also if we divide 62 by 2 then we will get 31. Therefore, 62 is the number which is divided by 2 and 31 .
Now we will come to the question. As we can see 5 and 12 are the two numbers which have only one common number as 1. Therefore, 5 and 12 are co prime to each other. The two numbers 5 and 12 will have their product as 60. Now we will divide 60 by 5 and we will get 12 also if we divide 60 by 12 then we will get 5. Therefore, 60 is the number which is divided by 5 and 12. Therefore, the number 60 is divisible by both 5 and 12 always.
Hence, the required number is 60.

Note: The numbers which are co prime will always have a product as a number which will always be divisible by both the numbers. If we come across a big number and we need to find the number which is divisible by both the numbers then we cannot convert the numbers into the simplest form also. This is because the two numbers will be co prime having 1 as a common factor. Simply just product the numbers and we will get the result. We will focus completely on the solution because if we do not then we will get the wrong product of the numbers and get the wrong answer.