Least Common Multiple of 48 and 60

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 60 the smallest integer that is 240 that is divisible by both numbers.

Least Common Multiple (LCM) of 48 and 60 is 240.

LCM(48,60) = 240

LCM of 48 and 60

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

LCM of:
and

Least Common Multiple of 48 and 60

LCM of 48 and 60 is 240

Least common multiple can be found by multiplying the highest exponent prime factors of 48 and 60. First we will calculate the prime factors of 48 and 60.

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 60


2 60
2 30
3 15
5 5
1

Prime factors of 60 are 2, 3,5. Prime factorization of 60 in exponential form is:

60 = 22×31×51

Now multiplying the highest exponent prime factors to calculate the LCM of 48 and 60.

LCM(48,60) = 24×31×51
LCM(48,60) = 240

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 60

List of positive integer factors of 60 that divides 60 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Least Common Multiple of 48 and 60 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 60, than apply into the LCM equation.

GCF(48,60) = 12
LCM(48,60) = ( 48 × 60) / 12
LCM(48,60) = 2880 / 12
LCM(48,60) = 240

Properties of LCM 48 and 60

(i) The LCM of 60 and 48 is associative

LCM of 48 and 60 = LCM of 60 and 48

Related Least Common Multiples of 48

Related Least Common Multiples of 60

Frequently Asked Questions on LCM of 48 and 60

1. What is the LCM of 48 and 60?

Answer: LCM of 48 and 60 is 240.

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 60?

Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.

4. How to Find the LCM of 48 and 60?

Answer:

Least Common Multiple of 48 and 60 = 240

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 60

60 = 2 x 2 x 3 x 5

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

LCM = 240 = 2 x 2 x 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 48 and 60 is 240.