LCM of 4 12 and 20

LCM of 4, 12 and 20 is 60. LCM or least common multiple is the smallest common multiple of two or more numbers. It is a method to find the smallest common multiple between any two or more numbers.

The LCM of 4,12 and 20 is the result of multiplying all prime factors, such that the greatest number of times they occur in either number

What is LCM of 4, 12 and 20

The Least Common Multiple or Lowest Common Multiple of 4,12 and 20 is 60.

LCM of 4 12 and 20

How to Find LCM of 4, 12 and 20?

Let us look at the different methods for finding the LCM of 4, 12 and 20

  • By Prime Factorisation
  • By Division method
  • By Listing the multiples

LCM of 4, 12 and 20 Using Prime Factorisation Method

Prime factorization is the process of finding the prime numbers which are multiplied together to get the original number.

Prime factorization of 4, 12 and 20 is:

4 = 2 x 2 = 22

12= 2 x 2 x 3 = 22 x 31

20 = 2 x 2 x 5 = 22 x 51

LCM of 4, 12 and 20 can be obtained by multiplying prime factors raised to their highest powers.

Hence, the LCM of 4, 12 and 20 by prime factorization is 60.

LCM of 4,12 and 20 by division method

To Calculate the LCM of 4,12 and 20 by division method,

Step 1: Divide the numbers 4, 12, 20 by the smallest prime number 2 to such that the smallest prime number should divide the number completely.

Step 2: Now we will again divide the quotient of step 1 by the smallest prime number.

Step 3: Repeat the step until the quotient becomes 1.

The LCM of 4, 12 and 20 by division method is 60.

2 4 12 20
2 2 6 10
3 1 3 5
5 1 1 5
1 1 1

LCM = 2 x 2 x 3 x 5 =60

LCM of 4, 12 and 20 by Listing Multiples

First to find the LCM of 4,12 and 20 let us list the multiples of 4,12 and 20.

Multiples of 4 : 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 60, 60, 64, …

Multiples of 12 : 12, 24, 36, 48, 60 ,72, 84, …

Multiples of 20 : 20, 40, 60, 80, 100, …

Step 1: List out a few multiples of 4, 12 and 20

Step 2: Now the common multiples from the multi[les of 4, 12 and 20 are 60, …

Step 3: The smallest common multiple of 4,12 and 20 is 60.

Hence the least common multiple of 4, 12 and 20 = 60

Related Articles

Video Lesson on Applications of LCM

Solved Example

Example:

Find the smallest number that is divisible by 4,12 and 20 exactly?

Solution:

The smallest number that is divisible by 4,12 and 20 exactly is their LCM

Therefore, the LCM of 4,12 and 20 is 60.

Frequently Asked Questions on LCM of 4,12 and 20

Q1

What is the LCM of 4, 12 and 20?

The LCM of 4, 12 and 20 is 60.
Q2

What are the Methods to find LCM of 4, 12 and 20?

The Commonly used methods to find the LCM of 4, 12, 20 are the listing of multiples, prime factorisation and division method.

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