# What is the LCM of 75 and 105?

To find the LCM of 75 and 105, we need the least number which is exactly divisible by both 75 and 105.

## Answer: LCM of 75 and 105 is 525

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 can find the LCM of the numbers in the following two ways.

### Method 1: LCM of 75 and 105 by Formula

The formula of LCM is LCM (a, b) = (a × b) / GCF (a, b)

The Greatest Common Factor (GCF) of (75, 105) = 15

So, GCF (75,105) = 15

By formula,

LCM (75, 105) = (75 × 105) / GCF (75, 105)

= (75 × 105) / 15

= 7875/15

= 525

So, LCM of 75 and 105 = 525

### Method 2: LCM of 75 and 105 by Listing Method

Let's see the first few multiples of 75 and 105 and identify the common multiples of 75 and 105.

The least among the common multiples is the LCM of 75 and 105.

Clearly, 525 is the least common multiple of 75 and 105.

Observe that the solution to our question LCM of 75 and 105 is the same in both methods.