LCM of 5 and 12 is 60. The least common multiple is a technique to find the smallest common multiple between any two or more numbers. It is used to add or subtract any two fractions when the denominators of the fractions are different. Experts explained the LCM of Two Numbers in an interactive way with the aim to provide the best learning experience for the students. Let us learn how to verify the least common multiple of 5 and 12 in a clear format in this article.
What is LCM of 5 and 12?
The answer to this question is 60.
How to Find LCM of 5 and 12?
The following methods are used to find the LCM of 5 and 12:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 5 and 12 Using Prime Factorisation Method
By prime factorisation method, we can write 5 and 12 as the product of prime numbers, such that;
5 = 5
12 = 2 × 2 × 3
LCM (5, 12) = 2 × 2 × 3 × 5 = 60
LCM of 5 and 12 Using Division Method
In this method, we divide the numbers 5 and 12 by their prime factors to find their LCM. The product of these divisors gives the least common multiple of 5 and 12. This can be shown as below.
|
2 |
5 |
12 |
|
2 |
5 |
6 |
|
3 |
5 |
3 |
|
5 |
5 |
1 |
|
x |
1 |
1 |
No more further division can be done.
Therefore, LCM (5, 12) = 2 × 2 × 3 × 5 = 60
LCM of 5 and 12 Using Listing the Multiples
To find the LCM of 5 and 12 using the method of listing the multiples, we write the multiples of 5 and 12 as shown in the below table.
|
Multiples of 5 |
Multiples of 12 |
|
5 |
12 |
|
10 |
24 |
|
15 |
36 |
|
20 |
48 |
|
25 |
60 |
|
30 |
72 |
|
35 |
84 |
|
40 |
96 |
|
45 |
108 |
|
50 |
120 |
|
55 |
132 |
|
60 |
144 |
|
65 |
156 |
LCM (5, 12) = 60
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved E×amples
Q. 1: Find the LCM of 5 and 12 by prime factorisation
Solution: 5 = 5
12 = 2 × 2 × 3
LCM (5, 12) = 2 × 2 × 3 × 5 = 60
Hence the LCM of 5 and 12 by prime factorisation is 60.
Q. 2: The GCD and LCM of the two numbers are 1 and 60. If one number is 5, calculate the other number.
Solution: Let the other number be m
We know that,
GCD × LCM = 5 × m
m = (GCD × LCM)/5
m = (1 × 60)/5
m = 60/5
m = 12
Hence the other number is 12.
Frequently Asked Questions on LCM of 5 and 12
What is the LCM of 5 and 12?
What are the methods used to find the LCM of 5 and 12?
The methods used to find the LCM of 5 and 12 are
Prime factorisation
Division method
Listing the multiples
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