LCM of 48 and 54 is 432. The Least Common Divisor(LCD), or Least Common Multiple(LCM) or Lowest Common Multiple(LCM) is the smallest positive number that is divisible by the given numbers. In the given set of numbers 48 and 54, 432 is the first(least or smallest) number that is common in the set of multiples of 48 and 54. You can use the HCF and LCM to understand the LCM.
What is LCM of 48 and 54
The Least Common Multiple or Lowest Common Multiple of 48 and 54 is 432.
How to Find LCM of 48 and 54?
LCM of 48 and 54 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 48 and 54 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 48 and 54 can be expressed as;
48 = 2 × 2 × 2 × 2 × 3
54 = 2 × 3 × 3 × 3
2 × 3 is the common factors of 48 and 54 which is multiplied by the other factors to get the LCM.
LCM (48, 54) = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
LCM of 48 and 54 Using Division Method
In the Division Method, the following steps are followed;
- Dividing 48 and 54 with smallest prime numbers and in increasing order of divisibility.
- When the division is complete with reminders as one, the prime divisors are multiplied to get the LCM.
|
2 |
48 |
54 |
|
2 |
24 |
27 |
|
2 |
12 |
27 |
|
2 |
6 |
27 |
|
3 |
3 |
27 |
|
3 |
1 |
9 |
|
3 |
1 |
3 |
|
× |
1 |
1 |
LCM (48, 54) = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
LCM of 48 and 54 Using Listing the Multiples
By listing all the multiples of 48 and 54, we can identify the/least common multiple(LCM). Below is the list of multiples for 48 and 54.
|
Multiples of 48 |
Multiples of 54 |
|
48 |
54 |
|
96 |
108 |
|
144 |
162 |
|
192 |
216 |
|
240 |
270 |
|
288 |
324 |
|
336 |
378 |
|
384 |
432 |
|
432 |
486 |
LCM (48, 54) = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 48 and 54?
Answer: 432 is the smallest number that is divisible by both 48 and 54.
What is the LCM for 2, 3, 48 and 54?
Answer: LCM for 2, 3, 48 and 54 is 432 as 2 and 3 are also the factors of 48 and 54.
Comments