Question

How to guess out - whether to useHCForLCMin a question.

Answer 1

We use HCF and LCM to find numbers for a given condition.
HCF is used when we want to obtain a number which is always less than or equal to the smallest number.
LCM is used when we want to obtain a number which is always greater than or equal to the biggest number.

For example,
We want to find the HCF and LCM of the numbers 60 and 72.
We start by writing each number as a product of its prime factors.
$60=2\times 2\times 3\times 5$
$72=2\times 2\times 2\times 3\times 3$
The highest common factor is found by multiplying all the factors which appear in both lists:
So the HCF of 60 and 72 is $2\times 2\times 3$ which is 12.
The lowest common multiple is found by multiplying all the factors which appear in either list:
So the LCM of 60 and 72 is 2 × 2 × 2 × 3 × 3 × 5 which is 360.