LCM of 48 and 108 is 432. LCM stands for the Least Common multiple or Lowest common multiple. LCM is the first positive number that is divisible by the given numbers. In the given set of numbers 48 and 108, 432 is the first(least or smallest) number that is common in the set of common multiples of 48 and 108. The LCM which is also known as LCD, Least Common Divisor for 48 and 108 is 432. You can read more on LCM for further details.
What is LCM of 48 and 108
The Least Common Multiple or Lowest Common Multiple of 48 and 108 is 432.
How to Find LCM of 48 and 108?
LCM of 48 and 108 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 48 and 108 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers 48 and 108 can be expressed as;
48 = 2 × 2 × 2 × 2 × 3
108 = 2 × 2 × 3 × 3 × 3
( 2 × 2 × 3) is the common prime factors, which is multiplied by (2 × 2 × 3 × 3) to get the LCM
LCM (48, 108) = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
LCM of 48 and 108 Using Division Method
In the Division Method,
- Dividing the numbers 48 and 108 by smallest prime divisors 2 and 3.
- Product of the prime divisors is the LCM
Division table shown below;
|
2 |
48 |
108 |
|
2 |
24 |
54 |
|
2 |
12 |
27 |
|
2 |
6 |
27 |
|
3 |
3 |
27 |
|
3 |
1 |
9 |
|
3 |
1 |
3 |
|
× |
1 |
1 |
Therefore LCM (48, 108) = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
LCM of 48 and 108 Using Listing the Multiples
By listing all the multiples of 48 and 108, we can look at the smallest common multiple, which is the LCM. Below is the list of multiples for 48 and 108
Multiples of 48
48, 96, 144, 192, 240, 288, 336, 384, 432, 480, 528
Multiples of 108
108, 216, 324, 432, 540, 648
LCM (48, 108) = 432
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 48 and 108?
Answer: 432 is the smallest number that is divisible by both 48 and 108.
What is the LCM for 4, 48 and 108?
Answer: LCM for 4, 48 and 108 is 432 as 4 is the factor of 48 and 108.
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