Question

Two numbers have these properties:

-Both numbers are greater than 6
-Their hcf is 6
-Their lcm is 60
What are the two numbers?

Answer 1

`12\ and\ 30`

Explanation:

Given both numbers are greater than 6

Their HCF is 6

Their LCM is 60

The product of the HCF and LCM of two numbers is the same as the product of the numbers themselves.

Let us say those number are
`a` and
`b`

`a* b=6* 60\\a* b=360`

So, the product of those number is
`360`

Let us factorize
`360`

`360=1* 2* 2* 3* 5* 6`

It is given that number should be greater than 6

The possible pairs of number are
`(10,36)\ and\ (12,30)`

But only
`(12,30)` has LCM as 60.

So those numbers are
`12\ and\ 30`