LCM of 24 and 60 is 120. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The smallest number among all common multiples of 24 and 60 is the LCM of 24 and 60. (24, 48, 72, 96, 120, 144, etc.) and (60, 120, 180, 240, 300, 360, etc.) are the first few multiples of 24 and 60, respectively. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 24 and 60?
The answer to this question is 120. The LCM of 24 and 60 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24 and 60, is the smallest positive integer 120 which is divisible by both 24 and 60 with no remainder.
How to Find LCM of 24 and 60?
LCM of 24 and 60 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24 and 60 Using Prime Factorisation Method
The prime factorisation of 24 and 60, respectively, is given by:
24 = (2 × 2 × 2 × 3) = 23 × 31 and
60 = (2 × 2 × 3 × 5) = 22 × 31 × 51
LCM (24, 60) = 120
LCM of 24 and 60 Using Division Method
We’ll divide the numbers (24, 60) by their prime factors to get the LCM of 24 and 60 using the division method (preferably common). The LCM of 24 and 60 is calculated by multiplying these divisors.
| 2 | 24 | 60 |
| 2 | 12 | 30 |
| 2 | 6 | 15 |
| 3 | 3 | 15 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (24, 60) = 120
LCM of 24 and 60 Using Listing the Multiples
To calculate the LCM of 24 and 60 by listing out the common multiples, list the multiples as shown below.
| Multiples of 24 | Multiples of 60 |
| 24 | 60 |
| 48 | 120 |
| 72 | 180 |
| 96 | 240 |
| 120 | 300 |
The smallest common multiple of 24 and 60 is 120.
Therefore LCM (24, 60) = 120
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LCM of 24 and 60 Solved Example
Question: Find the smallest number that is divisible by 24 and 60 exactly.
Solution:
The smallest number that is divisible by 24 and 60 exactly is their LCM.
⇒ Multiples of 24 and 60:
Multiples of 24 = 24, 48, 72, 96, 120, . . . .
Multiples of 60 = 60, 120, 180, 240, 300, . . . .
Therefore, the LCM of 24 and 60 is 120.
Frequently Asked Questions on LCM of 24 and 60
What is the LCM of 24 and 60?
List the methods used to find the LCM of 24 and 60.
Which of the following is the LCM of 24 and 60? 120, 28, 18, 2
What is the Least Perfect Square Divisible by 24 and 60?
LCM of 24 and 60 = 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5] ⇒ Least perfect square divisible by each 24 and 60 = LCM(24, 60) × 2 × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60] Therefore, 3600 is the required number.
If the LCM of 60 and 24 is 120, Find its GCF.
Since the LCM of 60 and 24 = 120
⇒ 120 × GCF(60, 24) = 1440
Therefore, the greatest common factor (GCF) = 1440/120 = 12.
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