Least Common Multiple of 24 and 38

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 38 the smallest integer that is 456 that is divisible by both numbers.

Least Common Multiple (LCM) of 24 and 38 is 456.

LCM(24,38) = 456

LCM of 24 and 38

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

LCM of:
and

Least Common Multiple of 24 and 38

LCM of 24 and 38 is 456

Least common multiple can be found by multiplying the highest exponent prime factors of 24 and 38. First we will calculate the prime factors of 24 and 38.

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 38


2 38
19 19
1

Prime factors of 38 are 2,19. Prime factorization of 38 in exponential form is:

38 = 21×191

Now multiplying the highest exponent prime factors to calculate the LCM of 24 and 38.

LCM(24,38) = 23×31×191
LCM(24,38) = 456

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 38

List of positive integer factors of 38 that divides 38 without a remainder.

1, 2, 19, 38

Least Common Multiple of 24 and 38 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 38, than apply into the LCM equation.

GCF(24,38) = 2
LCM(24,38) = ( 24 × 38) / 2
LCM(24,38) = 912 / 2
LCM(24,38) = 456

Properties of LCM 24 and 38

(i) The LCM of 38 and 24 is associative

LCM of 24 and 38 = LCM of 38 and 24

Related Least Common Multiples of 24

Related Least Common Multiples of 38

Frequently Asked Questions on LCM of 24 and 38

1. What is the LCM of 24 and 38?

Answer: LCM of 24 and 38 is 456.

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 38?

Answer: Factors of 38 are 1, 2, 19, 38. There are 4 integers that are factors of 38. The greatest factor of 38 is 38.

4. How to Find the LCM of 24 and 38?

Answer:

Least Common Multiple of 24 and 38 = 456

Step 1: Find the prime factorization of 24

24 = 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 38

38 = 2 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 = 456 = 2 x 2 x 2 x 3 x 19

Step 4: Therefore, the least common multiple of 24 and 38 is 456.