LCM of 3, 6, 9 and 12 is 36. LCM stands for Least Common Multiple or the Lowest common multiple, also known as LCD Least Common Divisor. LCM/LCD is the positive number that is a common multiple for the given set of numbers. Here the given set of numbers are 3, 6, 9 and 12. The smallest common multiple for all these numbers among many is 36, and hence it is the LCM. 72, 108, 144 are also the common multiples. You can refer to Multiples.
What is LCM of 3, 6, 9 and 12
The Least Common Multiple or Lowest Common Multiple of 3, 6, 9 and 12 is 36.
How to Find LCM of 3, 6, 9 and 12?
LCM of 3, 6, 9 and 12 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 6, 9 and 12 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 3, 6, 9 and 12 can be expressed as;
3 = 1 × 3
6 = 2 × 3
9 = 3 × 3
12 = 2 × 2 × 3
By multiplying the common and uncommon multiples of 3, 6 9 and 12, LCM is obtained.
LCM (3, 6, 9 and 12) = 2 × 2 × 3 × 3 = 36
LCM of 3, 6, 9 and 12 Using Division Method
For the numbers 3, 6, 9 and 12, to calculate the LCM by the Division Method, the given set of numbers are divided by prime factors. The product of prime divisors is the LCM.
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LCM (3, 6, 9 and 12) = 2 × 2 × 3 × 3 = 36
LCM of 3, 6, 9 and 12 Using Listing the Multiples
By listing all the multiples of 3, 6, 9 and 12, we can identify the least common multiple, which is the LCM. Below is the list of multiples for 3, 6, 9 and 12
Multiples of 3
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, ..
Multiples of 6
6, 12, 18, 24, 30, 36, 42, 48, 54…
Multiples of 9
9, 18, 27, 36, 45, 54….
Multiples of 12
12, 24, 36, 48…..
LCM (3, 6, 9 and 12) = 36
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, 6, 9 and 12?
Answer: 36 is the smallest number that is divisible by 3, 6, 9 and 12.
What is the LCM of 3 and 36?
Answer: LCM of 3 and 36 is 36.
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