# What is the LCM of 100 and 190?

To find the LCM of 100 and 190, we need the least number which is exactly divisible by both 100 and 190 without leaving any remainder.

## Answer: LCM of 100 and 190 is 1900

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

## Explanation:

We will use two methods to find the least common multiple of 100 and 190.

- LCM of 100 and 190 by Listing Method
- LCM of 100 and 190 by Formula

### Method 1: LCM of 100 and 190 by Listing Method

We will list the first few multiples of 100 and 190 and determine the common multiples.

The least among the common multiples is the LCM of 100 and 190

**Multiples of 100:**

100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, __ 1900__, 2000, 2100

**Multiples of 190:**

190, 380, 570, 760, 950, 1140, 1330, 1520, 1710, ** 1900**, 2090, 2280

Here, 1900 is the least common multiple of 100 and 190. So, the LCM of 100 and 190 is 1900.

### Method 2: LCM of 100 and 190 by Formula

The formula of LCM is

LCM (a,b) = (a × b) / GCF (a,b)

The Greatest Common Factor (GCF) of (100, 190) is 10. So, GCF (100, 190) = 10

So, the LCM of 100 and 190 by using the formula,

LCM (100, 190) = (100 × 190) / 10

= 10 × 190

= 1900

LCM of 100 and 190 = 1900

Observe that the solution to our question LCM of 100 and 190 is the same in both methods.