Least Common Multiple of 48 and 54

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 48 and 54 the smallest integer that is 432 that is divisible by both numbers.

Least Common Multiple (LCM) of 48 and 54 is 432.

LCM(48,54) = 432

LCM of 48 and 54

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 48 and 54

LCM of 48 and 54 is 432

Least common multiple can be found by multiplying the highest exponent prime factors of 48 and 54. First we will calculate the prime factors of 48 and 54.

Prime Factorization of 48


2 48
2 24
2 12
2 6
3 3
1

Prime factors of 48 are 2,3. Prime factorization of 48 in exponential form is:

48 = 24×31

Prime Factorization of 54


2 54
3 27
3 9
3 3
1

Prime factors of 54 are 2,3. Prime factorization of 54 in exponential form is:

54 = 21×33

Now multiplying the highest exponent prime factors to calculate the LCM of 48 and 54.

LCM(48,54) = 24×33
LCM(48,54) = 432

Factors of 48

List of positive integer factors of 48 that divides 48 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 54

List of positive integer factors of 54 that divides 54 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54

Least Common Multiple of 48 and 54 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 48 and 54, than apply into the LCM equation.

GCF(48,54) = 6
LCM(48,54) = ( 48 × 54) / 6
LCM(48,54) = 2592 / 6
LCM(48,54) = 432

Properties of LCM 48 and 54

(i) The LCM of 54 and 48 is associative

LCM of 48 and 54 = LCM of 54 and 48

Related Least Common Multiples of 48

Related Least Common Multiples of 54

Frequently Asked Questions on LCM of 48 and 54

1. What is the LCM of 48 and 54?

Answer: LCM of 48 and 54 is 432.

2. What are the Factors of 48?

Answer: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 10 integers that are factors of 48. The greatest factor of 48 is 48.

3. What are the Factors of 54?

Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.

4. How to Find the LCM of 48 and 54?

Answer:

Least Common Multiple of 48 and 54 = 432

Step 1: Find the prime factorization of 48

48 = 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 54

54 = 2 x 3 x 3 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 432 = 2 x 2 x 2 x 2 x 3 x 3 x 3

Step 4: Therefore, the least common multiple of 48 and 54 is 432.