LCM of 5, 6 and 8 is 120. In Mathematics, the LCM is the value evenly divisible by the numbers given. The Least common multiple of 5, 6 and 8 is the smallest number calculated from the common multiples. (5, 10, 15, 20, 25, ….), (6, 12, 18, 24, 30, ….) and (8, 16, 24, 32, 40,….) are the multiples of 5, 6 and 8. We can find the LCM effortlessly using the prime factorisation method, division method and by listing the multiples.
Also read: Least common multiple
What is LCM of 5, 6 and 8?
The answer to this question is 120. The LCM of 5, 6 and 8 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 5, 6 and 8, is the smallest positive integer 120 which is divisible by both 5, 6 and 8 with no remainder.
How to Find LCM of 5, 6 and 8?
LCM of 5, 6 and 8 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 5, 6 and 8 Using Prime Factorisation Method
The prime factorisation of 5, 6 and 8, respectively, is given by:
5 = 5¹
6 = 2 x 3 = 2¹ x 3¹
8 = 2 x 2 x 2 = 2³
LCM (5, 6, 8) = 120
LCM of 5, 6 and 8 Using Division Method
We’ll divide the numbers (5, 6, 8) by their prime factors to get the LCM of 5, 6 and 8 using the division method (preferably common). The LCM of 5, 6 and 8 is calculated by multiplying these divisors.
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No further division can be done.
Hence, LCM (5, 6, 8) = 120
LCM of 5, 6 and 8 Using Listing the Multiples
To calculate the LCM of 5, 6 and 8 by listing out the common multiples, list the multiples as shown below
- Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 110, 115, 120, . . . .
- Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . ., 96, 102, 108, 114, 120, . . . .
- Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, . . . ., 96, 104, 112, 120, . . . .
The smallest common multiple of 5, 6 and 8 is 120.
Therefore LCM (5, 6, 8) = 120
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Video Lesson on Applications of LCM
LCM of 5, 6 and 8 Solved Examples
Question: In 20, 350, 120, 280, what is the LCM of 5, 6 and 8?
Solution:
The LCM value is the smallest number which is divisible exactly by 5, 6 and 8
The number 120 satisfies this condition
Hence, the LCM is 120.
Frequently Asked Questions on LCM of 5, 6 and 8
What is the LCM of 5, 6 and 8?
Mention the methods used to determine the LCM of 5, 6 and 8.
Calculate the GCF if the LCM of 5, 6 and 8 is 120.
LCM x GCF = 5 x 6 x 8
Given
LCM of 5, 6 and 8 = 120
120 x GCF = 240
GCF = 240/120 = 2
Write the relation between GCF and LCM of 5, 6 and 8.
The relation between GCF and LCM of 5, 6 and 8 is
GCF x LCM = 5 x 6 x 8
GCF x LCM = 240
Find the LCM of 5, 6 and 8 using prime factorisation.
Using prime factorisation
5 = 5¹
6 = 2 x 3 = 2¹ x 3¹
8 = 2 x 2 x 2 = 2³
LCM of 5, 6 and 8 is 120.
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