Answer:
[tex]12\ and\ 30[/tex]
Step-by-step 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 [tex]a[/tex] and [tex]b[/tex]
[tex]a\times b=6\times 60\\a\times b=360[/tex]
So, the product of those number is [tex]360[/tex]
Let us factorize [tex]360[/tex]
[tex]360=1\times 2\times 2\times 3\times 5\times 6[/tex]
It is given that number should be greater than 6
The possible pairs of number are [tex](10,36)\ and\ (12,30)[/tex]
But only [tex](12,30)[/tex] has LCM as 60.
So those numbers are [tex]12\ and\ 30[/tex]
