LCM of 42 and 72 is 504. The number divisible evenly by 42 and 72 is the LCM value. The Least common multiple of 42 and 72 found using the common multiples are discussed briefly here. The multiples of 42 are (42, 84, 126, 168, 210, 252, ….) and the multiples of 72 are (72, 144, 216, 288, 360, 432, ….) respectively. Prime factorisation, listing of the multiples and division are the methods used to find the LCM.
Also read: Least common multiple
What is LCM of 42 and 72?
The answer to this question is 504. The LCM of 42 and 72 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 42 and 72, is the smallest positive integer 504 which is divisible by both 42 and 72 with no remainder.
How to Find LCM of 42 and 72?
LCM of 42 and 72 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 42 and 72 Using Prime Factorisation Method
The prime factorisation of 42 and 72, respectively, is given by:
42 = 2 x 3 x 7 = 2¹ x 3¹ x 7¹
72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²
LCM (42, 72) = 504
LCM of 42 and 72 Using Division Method
We’ll divide the numbers (42, 72) by their prime factors to get the LCM of 42 and 72 using the division method (preferably common). The LCM of 42 and 72 is calculated by multiplying these divisors.
|
2 |
42 |
72 |
|
2 |
21 |
36 |
|
2 |
21 |
18 |
|
3 |
21 |
9 |
|
3 |
7 |
3 |
|
7 |
7 |
1 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (42, 72) = 504
LCM of 42 and 72 Using Listing the Multiples
To calculate the LCM of 42 and 72 by listing out the common multiples, list the multiples as shown below
Multiples of 42 = 42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504, ………
Multiples of 72 = 72, 144, 216, 288, 360, 432, 504, ……
LCM (42, 72) = 504
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Video Lesson on Applications of LCM
LCM of 42 and 72 Solved Examples
Question: If the GCD is 6, LCM is 504 and one number is 42, determine the other.
Solution:
Given
GCD = 6
LCM = 504
One number = 42
Consider y as the other number
LCM x GCD = 42 x y
y = (LCM x GCD)/42
y = (504 x 6)/42
y = 72
Hence, the other number is 72.
Frequently Asked Questions on LCM of 42 and 72
What is the LCM of 42 and 72?
What is the GCF if the LCM of 42 and 72 is 504?
LCM x GCF = 42 x 72
Given
LCM of 42 and 72 is 504
504 x GCF = 3024
GCF = 3024/504 = 6
List the methods used to find the LCM of 42 and 72.
Using prime factorisation, find the LCM of 42 and 72.
Using prime factorisation,
42 = 2 x 3 x 7
72 = 2 x 2 x 2 x 3 x 3
LCM of 42 and 72 = 504
Determine the LCM of 42 and 72.
LCM of 42 and 72 can be found by listing the multiples
(42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504, ….) are the multiples of 42
(72, 144, 216, 288, 360, 432, 504, …) are the multiples of 72
LCM of 42 and 72 is 504.
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