LCM of 3, 4 and 5 is 60. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values.The smallest number among all common multiples of 3, 4, and 5 is the LCM of 3, 4, and 5. (3, 6, 9, 12, 15…), (4, 8, 12, 16, 20…), and (5, 10, 15, 20, 25…), respectively, are the first few multiples of 3, 4, and 5. To find the LCM of 3, 4, 5, there are three main methods: listing multiples, division method, and prime factorization. Prime factorization, listing multiples, and division are the three most frequent methods for determining the LCM of 3, 4, and 5.
Also read: Least common multiple
What is LCM of 3, 4 and 5?
The answer to this question is 360. The LCM of 3, 4 and 5 using various methods is shown in this article for your reference. The LCM of three non-zero integers, 3, 4 and 5, is the smallest positive integer 60 which is divisible by both 3, 4 and 5 with no remainder.
How to Find LCM of 3, 4 and 5?
LCM of 3, 4 and 5 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 4 and 5 Using Prime Factorisation Method
The prime factorisation of 3, 4 and 5, respectively, is given by:
(3) = 31, (2 × 2) = 22, and (5) = 51
LCM (3, 4, 5) = 60
LCM of 3, 4 and 5 Using Division Method
We’ll divide the numbers (3, 4, 5) by their prime factors to get the LCM of 3, 4 and 5 using the division method (preferably common). The LCM of 3, 4 and 5 is calculated by multiplying these divisors.
| 2 | 3 | 4 | 5 |
| 2 | 3 | 2 | 5 |
| 3 | 3 | 1 | 5 |
| 5 | 1 | 1 | 5 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (3, 4, 5) = 60
LCM of 3, 4 and 5 Using Listing the Multiples
To calculate the LCM of 3, 4 and 5 by listing out the common multiples, list the multiples as shown below.
| Multiples of 3 | Multiples of 4 | Multiples of 5 |
| 3 | 4 | 5 |
| 6 | 8 | 10 |
| 9 | 12 | 15 |
| 12 | 16 | 20 |
| 15 | 20 | 25 |
| …… | ……. | … |
| …… | … | ….. |
| 60 | 60 | 60 |
The smallest common multiple of 3, 4 and 5 is 60.
LCM (3, 4, 5) = 60
Related Articles
Video Lesson on Applications of LCM
LCM of 3, 4 and 5 Solved Example
Question: Find the smallest number that is divisible by 3, 4, 5 exactly.
Solution:
The value of LCM(3, 4, 5) will be the smallest number that is exactly divisible by 3, 4, and 5.
⇒ Multiples of 3, 4, and 5:
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 48, 51, 54, 57, 60, . . . .
Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . ., 52, 56, 60, . . . .
Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 45, 50, 55, 60, . . . .
Therefore, the LCM of 3, 4, and 5 is 60.
Comments