LCM of 5, 10, 15 and 20 is 60. The LCM is a very important concept in Mathematics and has a wide application in our daily lives. Least common multiple of 5, 10, 15 and 20 is the smallest number which we get from the common multiples. (5, 10, 15, 20, 25, ….), (10, 20, 30, 40, 50,….), (15, 30, 45, 60, 75, …..) and (20, 40, 60, 80, 100, …..) are the first few multiples of 5, 10, 15 and 20. The LCM can be found by using methods such as division, prime factorisation and by listing the multiples.
Also read: Least common multiple
What is LCM of 5, 10, 15 and 20?
The answer to this question is 60. The LCM of 5, 10, 15 and 20 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 5, 10, 15 and 20, is the smallest positive integer 60 which is divisible by both 5, 10, 15 and 20 with no remainder.
How to Find LCM of 5, 10, 15 and 20?
LCM of 5, 10, 15 and 20 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 5, 10, 15 and 20 Using Prime Factorisation Method
The prime factorisation of 5, 10, 15 and 20, respectively, is given by:
5 = 5¹
10 = 2 x 5 = 2¹ x 5¹
15 = 3 x 5 = 3¹ x 5¹
20 = 2 x 2 x 5 = 2² x 5¹
LCM (5, 10, 15, 20) = 60
LCM of 5, 10, 15 and 20 Using Division Method
We’ll divide the numbers (5, 10, 15, 20) by their prime factors to get the LCM of 5, 10, 15 and 20 using the division method (preferably common). The LCM of 5, 10, 15 and 20 is calculated by multiplying these divisors.
| 2 | 5 | 10 | 15 | 20 |
| 3 | 5 | 5 | 15 | 10 |
| 5 | 5 | 5 | 5 | 10 |
| 2 | 1 | 1 | 1 | 2 |
| x | 1 | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (5, 10, 15, 20) = 60
LCM of 5, 10, 15 and 20 Using Listing the Multiples
To calculate the LCM of 5, 10, 15 and 20 by listing out the common multiples, list the multiples as shown below
| Multiples of 5 | Multiples of 10 | Multiples of 15 | Multiples of 20 |
| 5 | 10 | 15 | 20 |
| 10 | 20 | 30 | 40 |
| 15 | 30 | 45 | 60 |
| 20 | 40 | 60 | 80 |
| 25 | 50 | 75 | 100 |
| 30 | 60 | 90 | 120 |
| 35 | 70 | 105 | 140 |
| 40 | 80 | 120 | 160 |
| 45 | 90 | 135 | 180 |
| 50 | 100 | 150 | 200 |
| 55 | 110 | 165 | 220 |
| 60 | 120 | 180 | 240 |
The smallest common multiple of 5, 10, 15 and 20 is 60.
Therefore LCM (5, 10, 15, 20) = 60
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LCM of 5, 10, 15 and 20 Solved Example
Question: Calculate the smallest number divisible by 5, 10, 15 and 20.
Solution:
The smallest number which is exactly divisible by 5, 10, 15 and 20 is the LCM.
Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, …..
Multiples of 10 = 10, 20, 30, 40, 50, 60, ….
Multiples of 15 = 15, 30, 45, 60, 75, ….
Multiples of 20 = 20, 40, 60, 80, 100, ….
Hence, the LCM is 60.
Frequently Asked Questions on LCM of 5, 10, 15 and 20
Using the prime factorisation, find the LCM of 5, 10, 15 and 20.
The LCM of 5, 10, 15 and 20 is 60.
Using the prime factorisation
5 = 5¹
10 = 2 x 5 = 2¹ x 5¹
15 = 3 x 5 = 3¹ x 5¹
20 = 2 x 2 x 5 = 2² x 5¹
LCM (5, 10, 15, 20) = 60
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