LCM of 8, 10 and 12 is 120. Students can grasp the steps used to determine the least common multiple of 8, 10 and 12 by going through the common multiples. (8, 16, 24, 32, 40, 48, ….), (10, 20, 30, 40, 50, 60, …..) and (12, 24, 36, 48, 60,….) are the multiples of 8, 10 and 12. The LCM of two numbers with the help of prime factorisation, listing the multiples and division are available here in a stepwise format.
Also read: Least common multiple
What is LCM of 8, 10 and 12?
The answer to this question is 120. The LCM of 8, 10 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8, 10 and 12, is the smallest positive integer 120 which is divisible by both 8, 10 and 12 with no remainder.
How to Find LCM of 8, 10 and 12?
LCM of 8, 10 and 12 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8, 10 and 12 Using Prime Factorisation Method
The prime factorisation of 8, 10 and 12, respectively, is given by:
8 = 2 x 2 x 2 = 2³
10 = 2 x 5 = 2¹ x 5¹
12 = 2 x 2 x 3 = 2² x 3¹
LCM (8, 10, 12) = 120
LCM of 8, 10 and 12 Using Division Method
We’ll divide the numbers (8, 10, 12) by their prime factors to get the LCM of 8, 10 and 12 using the division method (preferably common). The LCM of 8, 10 and 12 is calculated by multiplying these divisors.
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2 |
8 |
10 |
12 |
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2 |
4 |
5 |
6 |
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2 |
2 |
5 |
3 |
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3 |
1 |
5 |
3 |
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5 |
1 |
5 |
1 |
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x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (8, 10, 12) = 120
LCM of 8, 10 and 12 Using Listing the Multiples
To calculate the LCM of 8, 10 and 12 by listing out the common multiples, list the multiples as shown below
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, . . . .
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, . . . .
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . .
LCM (8, 10, 12) = 120
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 8, 10 and 12 Solved Examples
Question: What is the smallest number divisible exactly by 8, 10 and 12?
Solution:
The smallest number divisible exactly by 8, 10 and 12 is the LCM value
Multiples of 8 = 8, 16, 24, 32, 40, 48, ……
Multiples of 10 = 10, 20, 30, 40, 50, …..
Multiples of 12 = 12, 24, 36, 48, 60, …..
Hence, the LCM is 120.
Frequently Asked Questions on LCM of 8, 10 and 12
From the numbers 10, 60, 120 and 80, what is the LCM of 8, 10 and 12?
Write the methods used to determine the LCM of 8, 10 and 12?
Show the relation between GCF and LCM of 8, 10 and 12.
The relation between GCF and LCM of 8, 10 and 12 is
LCM x GCF = 8 x 10 x 12
LCM x GCF = 840
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