LCM of 5, 15 and 20 is 60. The Least Common Divisor (LCD) also known as Least Common multiple or Lowest Common Multiple simply known as LCM is the smallest or the least positive integer that is common to the set of numbers. In the given set of numbers 5, 15 and 20, 60 is the first(least or smallest) number that is common in the set of multiples of 5, 15 and 20. 120, 180.. are also common multiples, however 60 is the LCM. You can refer to Multiples.
What is LCM of 5, 15 and 20
The Least Common Multiple or Lowest Common Multiple of 5, 15 and 20 is 60.
How to Find LCM of 5, 15 and 20?
LCM of 5, 15 and 20 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 5, 15 and 20 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 5, 15 and 20 can be expressed as;
5 = 1 × 5
15 = 3 × 5
20 = 2 × 2 × 5
Here 5 is common and 2, 2 and 3 are uncommon factors. LCM is formed by all these factors.
Therefore, LCM(5, 15 and 20) = 2 × 2 × 3 × 5 = 60
LCM of 5, 15 and 20 Using Division Method
In the Division Method, the given set of numbers 5, 15 and 20 are divided by prime divisors in the increasing order. The division is stopped when the remainders become 1. The product of all the prime divisors, forms the LCM.
|
2 |
5 |
15 |
20 |
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2 |
5 |
15 |
10 |
|
3 |
5 |
15 |
5 |
|
5 |
5 |
5 |
5 |
|
× |
1 |
1 |
1 |
LCM (5, 15 and 20) = 2 × 2 × 3 × 5 = 60
LCM of 5, 15 and 20 Using Listing the Multiples
By listing all the multiples of 5, 15 and 20, we can identify the first common multiple, which is the LCM. Below is the list of multiples for 5, 15 and 20
Multiples of 5
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70
Multiples of 15
15, 30, 45, 60, 75, 90
Multiples of 20
20, 40, 60, 80, 100
LCM (5, 15 and 20) = 60
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 5, 15 and 20?
Answer: 60 is the smallest number that is divisible by 5, 15 and 20.
What is the LCM of 20 and 60?
Answer: LCM of 20 and 60 is 60.
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