LCM of 8, 12, 15 and 20 is 120. Students can grasp the methods used in calculating the least common multiple of 8, 12, 15 and 20 by listing the common multiples. (8, 16, 24, 32, 40, ….), (12, 24, 36, 48, 60, …..), (15, 30, 45, 60, 75, ….) and (20, 40, 60, 80, 100,….) are the multiples of 8, 12, 15 and 20. Students can learn the ways to find the LCM of two numbers using prime factorisation, by listing the multiples and division by referring to the study materials offered at BYJU’S for free.
Also read: Least common multiple
What is LCM of 8, 12, 15 and 20?
The answer to this question is 120. The LCM of 8, 12, 15 and 20 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 8, 12, 15 and 20, is the smallest positive integer 120 which is divisible by both 8, 12, 15 and 20 with no remainder.
How to Find LCM of 8, 12, 15 and 20?
LCM of 8, 12, 15 and 20 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 8, 12, 15 and 20 Using Prime Factorisation Method
The prime factorisation of 8, 12, 15 and 20, respectively, is given by:
8 = 2 x 2 x 2 = 2³
12 = 2 x 2 x 3 = 2² x 3¹
15 = 3 x 5 = 3¹ x 5¹
20 = 2 x 2 x 5 = 2² x 5¹
LCM (8, 12, 15, 20) = 120
LCM of 8, 12, 15 and 20 Using Division Method
We’ll divide the numbers (8, 12, 15, 20) by their prime factors to get the LCM of 8, 12, 15 and 20 using the division method (preferably common). The LCM of 8, 12, 15 and 20 is calculated by multiplying these divisors.
|
2 |
8 |
12 |
15 |
20 |
|
2 |
4 |
6 |
15 |
10 |
|
2 |
2 |
3 |
15 |
5 |
|
3 |
1 |
3 |
15 |
5 |
|
5 |
1 |
1 |
5 |
5 |
|
x |
1 |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (8, 12, 15, 20) = 120
LCM of 8, 12, 15 and 20 Using Listing the Multiples
To calculate the LCM of 8, 12, 15 and 20 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 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . .
Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, . . . .
Multiples of 20 = 20, 40, 60, 80, 100, 120, 140, . . . .
LCM (8, 12, 15, 20) = 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, 12, 15 and 20 Solved Examples
Question: What is the smallest number that when divided by 8, 12, 15 and 20 leaves a remainder as 6 in each case?
Solution:
LCM of 8, 12, 15 and 20 is the smallest number exactly divisible by the given numbers
We can write the smallest number when divided by 8, 12, 15 and 20 when divided gives a remainder 6 as
LCM of 8, 12, 15 and 20 + 6
8 = 2 x 2 x 2 = 2³
12 = 2 x 2 x 3 = 2² x 3¹
15 = 3 x 5 = 3¹ x 5¹
20 = 2 x 2 x 5 = 2² x 5¹
Here LCM of 8, 12, 15 and 20 + 6 = 120 + 6 = 126
Hence, the required number is 126.
Frequently Asked Questions on LCM of 8, 12, 15 and 20
From the numbers 50, 35, 120, 30, what is the LCM of 8, 12, 15 and 20?
Which are the methods used to determine the LCM of 8, 12, 15 and 20?
Using the listing of multiples, find the LCM of 8, 12, 15 and 20.
First let us list out the multiples
(8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, . . . .) are the multiples of 8
(12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . .) are the multiples of 12
(15, 30, 45, 60, 75, 90, 105, 120, . . . .) are the multiples of 15
(20, 40, 60, 80, 100, 120, 140, . . . .) are the multiples of 20
Hence, the LCM is 120.
What is the LCM of 8, 12, 15 and 20?
Determine the LCM of 8, 12, 15 and 20 using prime factorisation.
Using prime factorisation,
8 = 2 x 2 x 2
12 = 2 x 2 x 3
15 = 3 x 5
20 = 2 x 2 x 5
Therefore, the LCM is 120.
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