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Least Common Multiple of 24 and 30

Free LCM Calculator determines the least common multiple (LCM) between 24 and 30 the smallest integer that is 120 that is divisible by both numbers.

Least Common Multiple (LCM) of 24 and 30 is 120.

LCM(24,30) = 120

LCM of 24 and 30

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

LCM of:
and

Least Common Multiple (LCM) of 24 and 30 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 24 and 30. First we will calculate the prime factors of 24 and 30.

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 30


2 30
3 15
5 5
1

Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

Now multiplying the highest exponent prime factors to calculate the LCM of 24 and 30.

LCM(24,30) = 23×31×51
LCM(24,30) = 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 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30

Least Common Multiple of 24 and 30 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 30, than apply into the LCM equation.

GCF(24,30) = 6
LCM(24,30) = ( 24 × 30) / 6
LCM(24,30) = 720 / 6
LCM(24,30) = 120

Properties of LCM 24 and 30

(i) The LCM of 30 and 24 is associative

LCM of 24 and 30 = LCM of 30 and 24

Frequently Asked Questions on LCM of 24 and 30

1. What is the LCM of 24 and 30?

Answer: LCM of 24 and 30 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 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

4. How to Find the LCM of 24 and 30?

Answer:

Least Common Multiple of 24 and 30 = 120

Step 1: Find the prime factorization of 24

24 = 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 30

30 = 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 30 is 120.