# What is LCM of 3, 5 and 12?

The LCM of 3, 5 and 12 is the least number that is exactly divisible by 3, 5 and 12. There are 3 methods to find the LCM of 3, 5 and 12 i.e. by prime factorization, listing multiples, and using LCM of two numbers.

## Answer: LCM of 3, 5, 12 is 60

**Explanation: **

The LCM is the smallest number which is exactly divisible by the given numbers. We can compute the LCM of 3, 5 and 12 in many ways, the most commonly used methods are listed below.

ā LCM Calculator

## Methods to Find LCM of 3, 5, 12

The methods to compute the LCM of 3, 5 and 12 are explained below.

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

### LCM of 3, 5 and 12 by Common Division Method

In this method, we divide 3, 5 and 12 simultaneously with prime numbers and stop it when we don't have a prime number to divide 3, 5, and 12.

### LCM of 3, 5 and 12 by Listing Some Multiples

In this method, we list the first few multiples of 3, 5, and 12 and identify the common multiples. The least among the common multiples is the LCM of 3, 5 and 12.

**Multiples of 3:**3, 6, 9, 12, 15, 18, 21, 24, 27, 30**Multiples of 5:**5, 10, 15, 20, 25, 30, 35, 40, 45, 50**Multiples of 12:**12, 24, 36, 48, 60, 72, 84, 96, 108, 120

We find that the 20^{th} multiple of 3, 12^{th} multiple of 5, and 5^{th} multiple of 12 are common with each other. This common number 60 is the least common multiple (LCM).

### LCM of 3, 5, 12 using LCM of 2 Numbers Formula

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

LCM(3, 5, 12) = LCM(LCM(3, 5), 12)

LCM(3, 5) = 15

Therefore, LCM of 3, 5 and 12 = LCM(3, 5, 12) = LCM(LCM(3, 5), 12) = LCM(15, 12) = 60

### Therefore, the LCM of 3, 5 and 12 is 60.

**ā Also Check:**

- LCM of 2, 4, 8 - LCM(2, 4, 8) = 8
- LCM of 4, 5, 6 - LCM(4, 5, 6) = 60
- LCM of 15, 25 - LCM(15, 25) = 75
- LCM of 9, 12 - LCM(9, 12) = 36
- LCM of 2, 4 - LCM(2, 4) = 4
- LCM of 8, 12 - LCM(8, 12) = 24
- LCM of 4, 8, 12 - LCM(4, 8, 12) = 24