Least Common Multiple of 48 and 57

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 57 the smallest integer that is 912 that is divisible by both numbers.

Least Common Multiple (LCM) of 48 and 57 is 912.

LCM(48,57) = 912

LCM of 48 and 57

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

LCM of:
and

Least Common Multiple of 48 and 57

LCM of 48 and 57 is 912

Least common multiple can be found by multiplying the highest exponent prime factors of 48 and 57. First we will calculate the prime factors of 48 and 57.

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 57


3 57
19 19
1

Prime factors of 57 are 3,19. Prime factorization of 57 in exponential form is:

57 = 31×191

Now multiplying the highest exponent prime factors to calculate the LCM of 48 and 57.

LCM(48,57) = 24×31×191
LCM(48,57) = 912

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 57

List of positive integer factors of 57 that divides 57 without a remainder.

1, 3, 19, 57

Least Common Multiple of 48 and 57 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 57, than apply into the LCM equation.

GCF(48,57) = 3
LCM(48,57) = ( 48 × 57) / 3
LCM(48,57) = 2736 / 3
LCM(48,57) = 912

Properties of LCM 48 and 57

(i) The LCM of 57 and 48 is associative

LCM of 48 and 57 = LCM of 57 and 48

Related Least Common Multiples of 48

Related Least Common Multiples of 57

Frequently Asked Questions on LCM of 48 and 57

1. What is the LCM of 48 and 57?

Answer: LCM of 48 and 57 is 912.

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 57?

Answer: Factors of 57 are 1, 3, 19, 57. There are 4 integers that are factors of 57. The greatest factor of 57 is 57.

4. How to Find the LCM of 48 and 57?

Answer:

Least Common Multiple of 48 and 57 = 912

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 57

57 = 3 x 19

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

LCM = 912 = 2 x 2 x 2 x 2 x 3 x 19

Step 4: Therefore, the least common multiple of 48 and 57 is 912.