LCM of 3, 6 and 7 is 42. For the given set of numbers 3, 6 and 7 the smallest common multiple for all these numbers is 42, and hence it is the LCM. 84, 126, 168 are also the common multiples. LCM stands for Least or Lowest Common Multiple also known as LCD Least Common Divisor is the positive integer that is a common multiple to the given set of numbers. You can refer to LCM for more details.
What is LCM of 3, 6 and 7
The Least Common Multiple or Lowest Common Multiple of 3, 6 and 7 is 42.
How to Find LCM of 3, 6 and 7?
LCM of 3, 6 and 7 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 6 and 7 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 3, 6 and 7 can be expressed as;
3 = 1 × 3
6 = 2 × 3
7 = 1 × 7
Here 3 and 7 are the prime numbers, 6 is the multiple of 2 and 3. 3 is common Hence the
LCM (3, 6 and 7) = 2 × 3 × 7 = 42
LCM of 3, 6 and 7 Using Division Method
In the Division Method, 3, 6 and 7 are divided by prime divisors and their product forms the LCM
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2 |
3 |
6 |
7 |
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3 |
3 |
3 |
7 |
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7 |
1 |
1 |
7 |
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× |
1 |
1 |
1 |
LCM (3, 6 and 7) = 2 × 3 × 7 = 42
LCM of 3, 6 and 7 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 3, 6 and 7
Multiples of 3
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48
Multiples of 6
6, 12, 18, 24, 30, 36, 42, 48, 54
Multiples of 7
7, 14, 21, 28, 35, 42, 49, 56
LCM (3, 6 and 7) = 42
Related Articles
- Multiples.
- 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 and 7?
Answer: 42 is the smallest number that is divisible by 3, 6 and 7.
What is the LCM of 3 and 42?
Answer: LCM of 3 and 42 is 42.
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