LCM of 3, 5 and 12 is 60. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. The smallest number among all frequent multiples of 3, 5, and 12 is the LCM of 3, 5, and 12. (3, 6, 9, 12, 15…), (5, 10, 15, 20, 25…), and (12, 24, 36, 48, 60…), respectively, are the first few multiples of 3, 5, and 12.
Also read: Least common multiple
What is LCM of 3, 5 and 12?
The answer to this question is 60. The LCM of 3, 5 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3, 5 and 12, is the smallest positive integer 60 which is divisible by both 3, 5 and 12 with no remainder.
How to Find LCM of 3, 5 and 12?
LCM of 3, 5 and 12 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 3, 5 and 12 Using Prime Factorisation Method
The prime factorisation of 3, 5 and 12, respectively, is given by:
(3) = 31, (5) = 51, and
12 = (2 × 2 × 3) = 22 × 31
LCM (3, 5, 12) = 60
LCM of 3, 5 and 12 Using Division Method
We’ll divide the numbers (3, 5, 12) by their prime factors to get the LCM of 3, 5 and 12 using the division method (preferably common). The LCM of 3, 5 and 12 is calculated by multiplying these divisors.
| 2 | 3 | 5 | 12 |
| 2 | 3 | 5 | 6 |
| 3 | 3 | 5 | 3 |
| 5 | 1 | 5 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (3, 5, 12) = 120
LCM of 3, 5 and 12 Using Listing the Multiples
To calculate the LCM of 3, 5 and 12 by listing out the common multiples, list the multiples as shown below
| Multiples of 3 | Multiples of 5 | Multiples of 12 |
| 3 | 5 | 12 |
| 6 | 10 | 24 |
| 9 | 15 | 36 |
| …… | …. | .. |
| 120 | 120 | 120 |
The smallest common multiple of 3, 5 and 12 is 120.
Therefore LCM Multiples of 5 = 120
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LCM of 3, 5 and 12 Solved Example
Question: Find the smallest number that is divisible by 3, 5, 12 exactly.
Solution:
The value of LCM(3, 5, 12) will be the smallest number that is exactly divisible by 3, 5, and 12.
⇒ Multiples of 3, 5, and 12:
Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 51, 54, 57, 60, . . . .
Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 45, 50, 55, 60, . . . .
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . ., 24, 36, 48, 60, . . . .
Therefore, the LCM of 3, 5, and 12 is 60.
Frequently Asked Questions on LCM of 3, 5 and 12
What is the LCM of 3, 5 and 12?
List the methods used to find the LCM of 3, 5 and 12.
What is the Relation Between GCF and LCM of 3, 5, 12?
How to Find the LCM of 3, 5, and 12 by Prime Factorization?
⇒ LCM of 3, 5, 12 = 2 × 2 × 3 × 5 = 60.
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