LCM of 48 and 60 is 240. The Least Common Divisor (LCD) also known as 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 48 and 60, 240 is the first(least or smallest) number that is common in the set of multiples of 48 and 60. You can refer to HCF and LCM to differentiate between LCM and HCF.
What is LCM of 48 and 60?
The Least Common Multiple or Lowest Common Multiple of 48 and 60 is 240.
How to Find LCM of 48 and 60?
LCM of 48 and 60 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 48 and 60 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 48 and 60 can be expressed as;
48 = 2 x 2 x 2 x 2 x 3
60 = 2 x 2 x 3 x 5
LCM (48, 60) = 2 x 2 x 2 x 2 x 3 x 5 = 240
LCM of 48 and 60 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 |
48 |
60 |
|
3 |
24 |
30 |
|
2 |
8 |
10 |
|
2 |
4 |
5 |
|
5 |
2 |
5 |
|
2 |
2 |
1 |
|
x |
1 |
1 |
Hence LCM (48, 60) = 2 x 2 x 2 x 2 x 3 x 5 = 240
LCM of 48 and 60 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 48 and 60
|
Multiples of 48 |
Multiples of 60 |
|
48 |
60 |
|
96 |
120 |
|
144 |
180 |
|
192 |
240 |
|
240 |
300 |
|
288 |
360 |
|
336 |
240 |
LCM (48, 60) = 240
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 48 and 60?
Answer: 240 is the smallest number that is divisible by both 48 and 60.
What is the LCM for 2, 48 and 60?
Answer: LCM for 2, 48 and 60 is 240.
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