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.
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.
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