LCM of 3, 4, 5 and 6 is 60. LCM stands for Least/Lowest Common Multiple. The other term for LCM is LCD, Lowest Common Divisor. LCM/LCD is the positive integer that is a common multiple to the given set of numbers. Here the given set of numbers are 3, 4, 5 and 6. The smallest common multiple for all these numbers among many is 60, and hence it is the LCM. 90, 120, 160 are also the common multiples. You can refer to Multiples.
What is LCM of 3, 4, 5 and 6
The Least Common Multiple or Lowest Common Multiple of 3, 4, 5 and 6 is 60.
How to Find LCM of 3, 4, 5 and 6?
LCM of 3, 4, 5 and 6 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 4, 5 and 6 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 3, 4, 5 and 6 can be expressed as;
3 = 1 × 3
4 = 2 × 2
5 = 1 × 5
6 = 2 × 3
The product of common and uncommon prime factors forms the LCM.
LCM (3, 4, 5 and 6) = 2 × 2 × 3 × 5 = 60
LCM of 3, 4, 5 and 6 Using Division Method
In the Division Method, the numbers 3, 4, 5 and 6 are divided by prime divisors until one remains. The prime divisor product forms the LCM.
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LCM (3, 4, 5 and 6) = 2 × 2 × 3 × 5 = 60
LCM of 3, 4, 5 and 6 Using Listing the Multiples
By listing all the multiples of 3, 4, 5 and 6, we can notice the first common multiple esily, which is the LCM. Below is the list of multiples for 3, 4, 5 and 6
Multiples of 3
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66
Multiples of 4
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68
Multiples of 5
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70
Multiples of 6
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72
LCM (3, 4, 5 and 6) = 60
Related Articles
- LCM
- HCF and LCM
- LCM Formula
- LCM Calculator
- Prime Factorization and Division method
- LCM with Examples
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 3, 4, 5 and 6?
Answer: 60 is the smallest number that is divisible by 3, 4, 5 and 6.
What is the LCM of 3 and 60?
Answer: LCM of 3 and 60 is 60 as 3 is a factor of 60.
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