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Least Common Multiple of 20 and 24

Free LCM Calculator determines the least common multiple (LCM) between 20 and 24 the smallest integer that is 120 that is divisible by both numbers.

Least Common Multiple (LCM) of 20 and 24 is 120.

LCM(20,24) = 120

LCM of 20 and 24

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

LCM of:
and

Least Common Multiple (LCM) of 20 and 24 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20 and 24. First we will calculate the prime factors of 20 and 24.

Prime Factorization of 20


2 20
2 10
5 5
1

Prime factors of 20 are 2,5. Prime factorization of 20 in exponential form is:

20 = 22×51

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

Now multiplying the highest exponent prime factors to calculate the LCM of 20 and 24.

LCM(20,24) = 23×31×51
LCM(20,24) = 120

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1, 2, 4, 5, 10, 20

Factors of 24

List of positive integer factors of 24 that divides 24 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24

Least Common Multiple of 20 and 24 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20 and 24, than apply into the LCM equation.

GCF(20,24) = 4
LCM(20,24) = ( 20 × 24) / 4
LCM(20,24) = 480 / 4
LCM(20,24) = 120

Properties of LCM 20 and 24

(i) The LCM of 24 and 20 is associative

LCM of 20 and 24 = LCM of 24 and 20

Frequently Asked Questions on LCM of 20 and 24

1. What is the LCM of 20 and 24?

Answer: LCM of 20 and 24 is 120.

2. What are the Factors of 20?

Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.

3. 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.

4. How to Find the LCM of 20 and 24?

Answer:

Least Common Multiple of 20 and 24 = 120

Step 1: Find the prime factorization of 20

20 = 2 x 2 x 5

Step 2: Find the prime factorization of 24

24 = 2 x 2 x 2 x 3

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 20 and 24 is 120.