LCM of 5 and 24 is 120. The common multiple divisible exactly by 5 and 24 is the LCM. You will understand how to find the least common multiple of 5 and 24 by referring to this article. The multiples of 5 are (5, 10, 15, 20, 25, 30, ….) and the multiples of 24 are (24, 48, 72, 96, 120, 144, 168, ….) respectively. Division, prime factorisation and listing of the multiples are the common methods used to get the LCM value.
Also read: Least common multiple
What is LCM of 5 and 24?
The answer to this question is 120. The LCM of 5 and 24 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 5 and 24, is the smallest positive integer 120 which is divisible by both 5 and 24 with no remainder.
How to Find LCM of 5 and 24?
LCM of 5 and 24 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 5 and 24 Using Prime Factorisation Method
The prime factorisation of 5 and 24, respectively, is given by:
5 = 5 = 5¹
24 = 2 x 2 x 2 x 3 = 2³ x 3¹
LCM (5, 24) = 120
LCM of 5 and 24 Using Division Method
We’ll divide the numbers (5, 24) by their prime factors to get the LCM of 5 and 24 using the division method (preferably common). The LCM of 5 and 24 is calculated by multiplying these divisors.
|
2 |
5 |
24 |
|
2 |
5 |
12 |
|
2 |
5 |
6 |
|
3 |
5 |
3 |
|
5 |
5 |
1 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (5, 24) = 120
LCM of 5 and 24 Using Listing the Multiples
To calculate the LCM of 5 and 24 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, . . . ., 100, 105, 110, 115, 120, . . . .
Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, . . . ., 72, 96, 120, . . . .
LCM (5, 24) = 120
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LCM of 5 and 24 Solved Examples
Question: If the product of two numbers is 120, find the LCM if the GCD is 1.
Solution:
It is given that
GCD = 1
Product of two numbers = 120
We know that
LCM x GCD = product of two numbers
LCM = product of two numbers/ GCD
LCM = 120/1
LCM = 120
Hence, the LCM is 120.
Frequently Asked Questions on LCM of 5 and 24
What is the LCM of 5 and 24?
If the LCM of 5 and 24 is 120, what is the GCF?
LCM x GCF = 5 x 24
Given;
LCM of 5 and 24 is 120
120 x GCF = 120
GCF = 120/120 = 1
List the methods used to find the LCM of 5 and 24.
The methods used to find the LCM of 5 and 24 are:
Division method
Prime Factorisation
Listing the multiples
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