# What is LCM of 12, 30 and 42?

LCM of 12, 30 and 42 is the least number that is exactly divisible by 12, 30 and 42. There are 3 methods to find the LCM of 12, 30 and 42 i.e. by prime factorization, listing multiples, and using LCM of two numbers.

## Answer: LCM of 12, 30, 42 is 420

**Explanation: **

The least common multiple is the smallest number which is exactly divisible by the given numbers. We can compute the LCM of 12, 30 and 42 in many ways, the most commonly used methods are listed below.

ā LCM Calculator

## Methods to Find LCM of 12, 30, 42

The methods to compute the LCM of 12, 30 and 42 are explained below.

- By Common Division Method
- By Listing Some Multiples
- By using LCM of 2 numbers

### LCM of 12, 30 and 42 by Common Division Method

In this method, we divide 12, 30 and 42 simultaneously with prime numbers and stop it when we don't have a prime number to divide 12, 30, and 42.

### LCM of 12, 30 and 42 by Listing Some Multiples

In this method, we list the first few multiples of 12, 30, and 42 and identify the common multiples. The least among the common multiples is the LCM of 12, 30 and 42.

**Multiples of 12:**12, 24, 36, 48, 60, 72, 84, 96, 108, 120**Multiples of 30:**30, 60, 90, 120, 150, 180, 210, 240, 270, 300**Multiples of 42:**42, 84, 126, 168, 210, 252, 294, 336, 378, 420

We find that the 35^{th} multiple of 12, 14^{th} multiple of 30, and 10^{th} multiple of 42 are common with each other. This common number 420 is the least common multiple (LCM).

### LCM of 12, 30 and 42 using LCM of 2 Numbers Formula

The formula of LCM is LCM(X, Y, Z) = LCM(LCM(X, Y), Z)

LCM(12, 30, 42) = LCM(LCM(12, 30), 42)

LCM(12, 30) = 60

Therefore, LCM of 12, 30 and 42 = LCM(12, 30, 42) = LCM(LCM(12, 30), 42) = LCM(60, 42) = 420

### Therefore, the LCM of 12, 30 and 42 is 420.

**ā Also Check:**

- LCM of 8, 12 - LCM(8, 12) = 24
- LCM of 2, 3, 5 - LCM(2, 3, 5) = 30
- LCM of 20, 25, 30 - LCM(20, 25, 30) = 300
- LCM of 10, 12 - LCM(10, 12) = 60
- LCM of 3, 12 - LCM(3, 12) = 12
- LCM of 24, 36 - LCM(24, 36) = 72
- LCM of 4, 8, 12 - LCM(4, 8, 12) = 24