LCM of 6 and 8 is 24. The least common multiple is the process to find the smallest common multiple between any two or more numbers. It is also used to add or subtract any two fractions when the denominators of the fraction are different. Hence Least Common Multiple is used to make the denominators common which makes the simplification process easier. Let us learn in detail how to find the Least Common Multiple of 6 and 8 by prime factorization, by division method and by listing multiples in this article.
What is LCM of 6 and 8?
The answer to this question is 24.
How to Find LCM of 6 and 8?
LCM of 6 and 8 can be determined by using the three methods shown below:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 6 and 8 Using Prime Factorisation Method
By prime factorisation method, we can write 6 and 8 as the product of prime numbers, such that;
6 = 2 × 3
8 = 2 × 2 × 2
LCM (6, 8) = 24
LCM of 6 and 8 Using Division Method
In this method, we divide the numbers 6 and 8 by their prime factors to find their LCM. The product of these divisors denotes the least common multiple of 6 and 8. This can be shown as below.
|
2 |
6 |
8 |
|
2 |
3 |
4 |
|
2 |
3 |
2 |
|
3 |
3 |
1 |
|
x |
1 |
1 |
No more further division can be done.
Hence, LCM (6, 8) = 2 × 2 × 2 × 3 = 24
LCM of 6 and 8 Using Listing the Multiples
Here we list out the multiples of 6 and 8 to find their least common multiple as shown below:
|
Multiples of 6 |
Multiples of 8 |
|
6 |
8 |
|
12 |
16 |
|
18 |
24 |
|
24 |
32 |
LCM (6, 8) = 24
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q.1 Determine the smallest number that is divisible by 6 and 8 e×actly.
Solution: The LCM of 6 and 8 is the smallest number that is divisible by 6 and 8 e×actly
Multiples of 6: 6, 12, 18, 24, 30, 36, 42….
Multiples of 8: 8, 16, 24, 32, 40, 48, 56….
Hence the LCM of 6 and 8 is 24.
Q.2: The numbers 2 and 24 are the GCF and LCM of two numbers respectively. If one number is 6, find the other number.
Solution: Let y be the other number
GCF × LCM = 6 × y
y = (GCF × LCM) / 6
y = (2 × 24) / 6
y = 8
Hence the other number is 8.
Frequently Asked Questions on LCM of 6 and 8
What is the LCM of 6 and 8?
The number 42 is the LCM of 6 and 8. True or False.
How do you find the LCM of 6 and 8 by Prime Factorization?
Prime factors of 6 = 2 × 3
Prime factors of 8 = 2 × 2 × 2
LCM = 2 × 2 × 2 × 3 = 24.
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