Least Common Multiple of 24 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 24 and 60 the smallest integer that is 120 that is divisible by both numbers.

Least Common Multiple (LCM) of 24 and 60 is 120.

LCM(24,60) = 120

LCM of 24 and 60

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

LCM of:
and

Least Common Multiple of 24 and 60

LCM of 24 and 60 is 120

Least common multiple can be found by multiplying the highest exponent prime factors of 24 and 60. First we will calculate the prime factors of 24 and 60.

Prime Factorization of 24


2 24
2 12
2 6
3 3
1

Prime factors of 24 are 2,3. Prime factorization of 24 in exponential form is:

24 = 23×31

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 24 and 60.

LCM(24,60) = 23×31×51
LCM(24,60) = 120

Factors of 24

List of positive integer factors of 24 that divides 24 without a remainder.

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

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 24 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 24 and 60, than apply into the LCM equation.

GCF(24,60) = 12
LCM(24,60) = ( 24 × 60) / 12
LCM(24,60) = 1440 / 12
LCM(24,60) = 120

Properties of LCM 24 and 60

(i) The LCM of 60 and 24 is associative

LCM of 24 and 60 = LCM of 60 and 24

Related Least Common Multiples of 24

Related Least Common Multiples of 60

Frequently Asked Questions on LCM of 24 and 60

1. What is the LCM of 24 and 60?

Answer: LCM of 24 and 60 is 120.

2. What are the Factors of 24?

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

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 24 and 60?

Answer:

Least Common Multiple of 24 and 60 = 120

Step 1: Find the prime factorization of 24

24 = 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 = 120 = 2 x 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 24 and 60 is 120.