LCM of 72 and 24 is 72. The Least Common multiple or Lowest common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 72 and 24, 72 is the first (least or smallest) number that is common in the set of multiples of 72 and 24. Even 144 is a common multiple of 72 and 24, however it is not the least or the smallest common multiple. The LCM is also known as LCD, Least Common Divisor for 72 and 24 is 72. You can read more on LCM for further details.
What is LCM of 72 and 24
The Least Common Multiple or Lowest Common Multiple of 72 and 24 is 72.
How to Find LCM of 72 and 24?
LCM of 72 and 24 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 72 and 24 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 72 and 24 can be expressed as;
72 = 2 × 2 × 2 × 3 × 3
24 = 2 × 2 × 2 × 3
LCM (72, 24) = 2 × 2 × 2 × 3 × 3 = 72
LCM of 72 and 24 Using Division Method
In the Division Method, the given set of numbers are written in the same row separated by a comma. These numbers are divided with the smallest number that divides all, until no further division is possible or only when prime numbers are left.
|
2 |
72 |
24 |
|
3 |
36 |
12 |
|
2 |
12 |
4 |
|
2 |
6 |
2 |
|
3 |
3 |
1 |
|
x |
1 |
1 |
Hence, LCM (72, 24) = 2 × 2 × 2 × 3 × 3 = 72
LCM of 72 and 24 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 72 and 24
|
Multiples of 72 |
Multiples of 24 |
|
72 |
24 |
|
144 |
48 |
|
216 |
72 |
LCM (72, 24) = 72
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 72 and 24?
Answer: 72 is the smallest number that is divisible by both 72 and 24.
What is the LCM for 12, 72 and 24?
Answer: LCM for 12, 72 and 24 is 72.
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