LCM of 8, 15 and 21 is 840. The value divisible by the given numbers evenly provides the LCM. From the common multiples, the least common multiple of 8, 15 and 21 can be found. The multiples of 8 are (8, 16, 24, 32, 40, 48, ….), the multiples of 15 are (15, 30, 45, 60, 75, …..) and the multiples of 21 are (21, 42, 63, 84, 105, ….) respectively. The methods to find the LCM value of the given numbers are prime factorisation, division and listing the multiples.
Also read: Least common multiple
What is LCM of 8, 15 and 21?
The answer to this question is 840. The LCM of 8, 15 and 21 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8, 15 and 21, is the smallest positive integer 840 which is divisible by both 8, 15 and 21 with no remainder.
How to Find LCM of 8, 15 and 21?
LCM of 8, 15 and 21 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8, 15 and 21 Using Prime Factorisation Method
The prime factorisation of 8, 15 and 21, respectively, is given by:
12 = 2 x 2 x 2 = 2³
15 = 3 x 5 = 3¹ x 5¹
21 = 3 x 7 = 3¹ x 7¹
LCM (8, 15, 21) = 840
LCM of 8, 15 and 21 Using Division Method
We’ll divide the numbers (8, 15, 21) by their prime factors to get the LCM of 8, 15 and 21 using the division method (preferably common). The LCM of 8, 15 and 21 is calculated by multiplying these divisors.
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2 |
8 |
15 |
21 |
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2 |
4 |
15 |
21 |
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2 |
2 |
15 |
21 |
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3 |
1 |
15 |
21 |
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5 |
1 |
5 |
7 |
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7 |
1 |
1 |
7 |
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x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (8, 15, 21) = 840
LCM of 8, 15 and 21 Using Listing the Multiples
To calculate the LCM of 8, 15 and 21 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, . . . ., 816, 824, 832, 840, . . . .
Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, . . . ., 810, 825, 840, . . . .
Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, . . . ., 798, 819, 840, . . . .
LCM (8, 15, 21) = 840
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LCM of 8, 15 and 21 Solved Examples
Question: From the numbers 15, 840, 2, 10, which is the LCM of 8, 15 and 21?
Solution:
The LCM value of 8, 15 and 21 is the smallest common multiple which is divisible exactly by the given numbers.
The number which satisfies this condition is 840.
Hence, the LCM is 840.
Frequently Asked Questions on LCM of 8, 15 and 21
If the LCM of 8, 15 and 21 is 840, what is its GCF?
We know that
LCM x GCF = 8 x 15 x 21
As LCM (8, 15, 21) is 840
840 x GCF = 2520
GCF = 2520/840 = 3
Find the LCM of 8, 15 and 21.
Show the relation between GCF and LCM of 8, 15 and 21.
The relation between GCF and LCM of 8, 15 and 21 is
LCM x GCF = 8 x 15 x 21
LCM x GCF = 2520
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