LCM of 10 and 24 is 120. Students can understand the steps used to find the least common multiple of 10 and 24 using the common multiples. (10, 20, 30, 40, 50, 60, ….) and (24, 48, 72, 96, 120, 144,….) are the multiples of 10 and 24. The LCM of two numbers using the prime factorisation method, listing the multiples and division method are given here in a systematic way.
Also read: Least common multiple
What is LCM of 10 and 24?
The answer to this question is 120. The LCM of 10 and 24 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 10 and 24, is the smallest positive integer 120 which is divisible by both 10 and 24 with no remainder.
How to Find LCM of 10 and 24?
LCM of 10 and 24 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10 and 24 Using Prime Factorisation Method
The prime factorisation of 10 and 24, respectively, is given by:
10 = 2 x 5 = 2¹ x 5¹
24 = 2 x 2 x 2 x 3 = 2³ x 3¹
LCM (10, 24) = 120
LCM of 10 and 24 Using Division Method
We’ll divide the numbers (10, 24) by their prime factors to get the LCM of 10 and 24 using the division method (preferably common). The LCM of 10 and 24 is calculated by multiplying these divisors.
|
2 |
10 |
24 |
|
2 |
5 |
12 |
|
2 |
5 |
6 |
|
3 |
5 |
3 |
|
5 |
5 |
1 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (10, 24) = 120
LCM of 10 and 24 Using Listing the Multiples
To calculate the LCM of 10 and 24 by listing out the common multiples, list the multiples as shown below
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, ……
Multiples of 24 = 24, 48, 72, 96, 120, 144, …..
LCM (10, 24) = 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 10 and 24 Solved Examples
Question: Show the smallest number exactly divisible by 10 and 24.
Solution:
The smallest number divisible exactly by 10 and 24 is the LCM value
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, ……
Multiples of 24 = 24, 48, 72, 96, 120, 144, …..
Hence, the LCM is 120.
Frequently Asked Questions on LCM of 10 and 24
From 20, 50, 120 and 30, find the LCM of 10 and 24.
What methods can be used to find the LCM of 10 and 24?
Write the relation between GCF and LCM of 10 and 24.
The relation between GCF and LCM of 10 and 24 is
LCM x GCF = 10 x 24
LCM x GCF = 240
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