Least Common Multiple of 24 and 25

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 25 the smallest integer that is 600 that is divisible by both numbers.

Least Common Multiple (LCM) of 24 and 25 is 600.

LCM(24,25) = 600

LCM of 24 and 25

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

LCM of:
and

Least Common Multiple of 24 and 25

LCM of 24 and 25 is 600

Least common multiple can be found by multiplying the highest exponent prime factors of 24 and 25. First we will calculate the prime factors of 24 and 25.

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 25


5 25
5 5
1

Prime factors of 25 are 5. Prime factorization of 25 in exponential form is:

25 = 52

Now multiplying the highest exponent prime factors to calculate the LCM of 24 and 25.

LCM(24,25) = 23×31×52
LCM(24,25) = 600

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 25

List of positive integer factors of 25 that divides 25 without a remainder.

1, 5, 25

Least Common Multiple of 24 and 25 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 25, than apply into the LCM equation.

GCF(24,25) = 1
LCM(24,25) = ( 24 × 25) / 1
LCM(24,25) = 600 / 1
LCM(24,25) = 600

Properties of LCM 24 and 25

(i) The LCM of 25 and 24 is associative

LCM of 24 and 25 = LCM of 25 and 24

Related Least Common Multiples of 24

Related Least Common Multiples of 25

Frequently Asked Questions on LCM of 24 and 25

1. What is the LCM of 24 and 25?

Answer: LCM of 24 and 25 is 600.

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 25?

Answer: Factors of 25 are 1, 5, 25. There are 3 integers that are factors of 25. The greatest factor of 25 is 25.

4. How to Find the LCM of 24 and 25?

Answer:

Least Common Multiple of 24 and 25 = 600

Step 1: Find the prime factorization of 24

24 = 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 25

25 = 5 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 = 600 = 2 x 2 x 2 x 3 x 5 x 5

Step 4: Therefore, the least common multiple of 24 and 25 is 600.