# What is the LCM and HCF of 120 and 90?

To find the LCM of 120 and 90, we need the least number which is exactly divisible by both 120 and 90 without leaving any remainder.

## Answer: LCM of 120 and 90 is 360 and the HCF of 120 and 90 is 30

The Least Common Multiple (LCM) of two numbers a and b is the smallest number which is divisible by a and b exactly.

**Explanation:**

We will use the Listing Multiples Method to calculate the LCM of 120 and 90.

We will list the first few multiples of 120 and 90 and determine the common multiples.

The least among the common multiples is the LCM of 120 and 90.

So, the LCM of 120 and 90 is 360.

We are using the formula LCM (a,b) = (a × b) / HCF (a,b) to calculate the HCF of 120 and 90

The LCM of (120, 90) is 360.

So, the HCF(Highest Common Factor) of 120 and 90 is calculated as,

LCM (a,b) = (a × b) / HCF (a,b)

360 = (120 × 90) / HCF (120,90)

HCF (120,90) = (120 × 90) / 360

= 30

HCF of 120 and 90 = 30