LCM of 3, 5 and 11 is 165. There can be many multiples that are common to any 2 or 3 numbers. For example if we consider the multiples of 4, they are also multiples of 2. i.e 4, 8, 12 and so on are divisible by 2 also. However, 4 is the first or smallest number that is a common multiple of 2 and 4. Therefore, 4 will be the LCM – Least/Lowest Common Multiple of 2 and 4. Similarly for the given set of numbers are 3, 5 and 11. The smallest common multiple for all these numbers among many is 165, and hence it is the LCM. 330, 660 are also the common multiples. You can refer to Multiples. LCM is also known as LCD Least Common Divisor.
What is LCM of 3, 5 and 11
The Least Common Multiple or Lowest Common Multiple of 3, 5 and 11 is 165.
How to Find LCM of 3, 5 and 11?
LCM of 3, 5 and 11 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 5 and 11 Using Prime Factorisation Method
In the Prime Factorisation method, 3, 5 and 11 can be expressed as;
3 = 1 × 3
5 = 1 × 5
11 = 1 × 11
Since all are prime numbers and there are no common factors, the product of 3, 7 and 11 forms the LCM.
LCM (3, 5 and 11) = 3 × 5 × 11 = 165
LCM of 3, 5 and 11 Using Division Method
In the Division Method, dividing 3, 5 and 11 with prime divisors. Since all the 3 numbers are prime numbers, the product of 3, 5 and 11 forms the LCM.
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3 |
3 |
5 |
11 |
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5 |
1 |
5 |
11 |
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11 |
1 |
1 |
11 |
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× |
1 |
1 |
1 |
LCM(3, 5 and 11) = 3 × 5 × 11 = 165
LCM of 3, 5 and 11 Using Listing the Multiples
By listing all the multiples of given numbers, we get the least common multiple, which is the LCM. Below is the list of multiples for 3, 5 and 11
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, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171
Multiples of 5
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175
Multiples of 11
11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187
LCM (3, 5 and 11) = 165
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, 5 and 11?
Answer: 165 is the smallest number that is divisible by 3, 5 and 11.
What is the LCM of 3 and 165?
Answer: LCM of 3 and 165 is 165 as 3 is the factor of 165.
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