Least Common Multiple of 24 and 31

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 31 the smallest integer that is 744 that is divisible by both numbers.

Least Common Multiple (LCM) of 24 and 31 is 744.

LCM(24,31) = 744

LCM of 24 and 31

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

LCM of:
and

Least Common Multiple of 24 and 31

LCM of 24 and 31 is 744

Least common multiple can be found by multiplying the highest exponent prime factors of 24 and 31. First we will calculate the prime factors of 24 and 31.

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 31


31 31
1

Prime factors of 31 are 31. Prime factorization of 31 in exponential form is:

31 = 311

Now multiplying the highest exponent prime factors to calculate the LCM of 24 and 31.

LCM(24,31) = 23×31×311
LCM(24,31) = 744

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 31

List of positive integer factors of 31 that divides 31 without a remainder.

1, 31

Least Common Multiple of 24 and 31 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 31, than apply into the LCM equation.

GCF(24,31) = 1
LCM(24,31) = ( 24 × 31) / 1
LCM(24,31) = 744 / 1
LCM(24,31) = 744

Properties of LCM 24 and 31

(i) The LCM of 31 and 24 is associative

LCM of 24 and 31 = LCM of 31 and 24

Related Least Common Multiples of 24

Related Least Common Multiples of 31

Frequently Asked Questions on LCM of 24 and 31

1. What is the LCM of 24 and 31?

Answer: LCM of 24 and 31 is 744.

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 31?

Answer: Factors of 31 are 1, 31. There are 2 integers that are factors of 31. The greatest factor of 31 is 31.

4. How to Find the LCM of 24 and 31?

Answer:

Least Common Multiple of 24 and 31 = 744

Step 1: Find the prime factorization of 24

24 = 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 31

31 = 31

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

LCM = 744 = 2 x 2 x 2 x 3 x 31

Step 4: Therefore, the least common multiple of 24 and 31 is 744.