Least Common Multiple of 24 and 39

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 39 the smallest integer that is 312 that is divisible by both numbers.

Least Common Multiple (LCM) of 24 and 39 is 312.

LCM(24,39) = 312

LCM of 24 and 39

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

LCM of:
and

Least Common Multiple of 24 and 39

LCM of 24 and 39 is 312

Least common multiple can be found by multiplying the highest exponent prime factors of 24 and 39. First we will calculate the prime factors of 24 and 39.

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 39


3 39
13 13
1

Prime factors of 39 are 3,13. Prime factorization of 39 in exponential form is:

39 = 31×131

Now multiplying the highest exponent prime factors to calculate the LCM of 24 and 39.

LCM(24,39) = 23×31×131
LCM(24,39) = 312

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 39

List of positive integer factors of 39 that divides 39 without a remainder.

1, 3, 13, 39

Least Common Multiple of 24 and 39 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 39, than apply into the LCM equation.

GCF(24,39) = 3
LCM(24,39) = ( 24 × 39) / 3
LCM(24,39) = 936 / 3
LCM(24,39) = 312

Properties of LCM 24 and 39

(i) The LCM of 39 and 24 is associative

LCM of 24 and 39 = LCM of 39 and 24

Related Least Common Multiples of 24

Related Least Common Multiples of 39

Frequently Asked Questions on LCM of 24 and 39

1. What is the LCM of 24 and 39?

Answer: LCM of 24 and 39 is 312.

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 39?

Answer: Factors of 39 are 1, 3, 13, 39. There are 4 integers that are factors of 39. The greatest factor of 39 is 39.

4. How to Find the LCM of 24 and 39?

Answer:

Least Common Multiple of 24 and 39 = 312

Step 1: Find the prime factorization of 24

24 = 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 39

39 = 3 x 13

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

LCM = 312 = 2 x 2 x 2 x 3 x 13

Step 4: Therefore, the least common multiple of 24 and 39 is 312.