Least Common Multiple of 5 and 24

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

• Least Common Multiple of 5 and 24 by Prime method
• Least Common Multiple of 5 and 24 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 24. First we will calculate the prime factors of 5 and 24.

Prime Factorization of 5

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

5 = 5¹

Prime Factorization of 24

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 5 and 24.

LCM(5,24) = 2³×3¹×5¹
LCM(5,24) = 120

Factors of 5

List of positive integer factors of 5 that divides 5 without a remainder.

1, 5

Factors of 24

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

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

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5 and 24, than apply into the LCM equation.

GCF(5,24) = 1
LCM(5,24) = ( 5 × 24) / 1
LCM(5,24) = 120 / 1
LCM(5,24) = 120

(i) The LCM of 24 and 5 is associative

LCM of 5 and 24 = LCM of 24 and 5

1. What is the LCM of 5 and 24?

Answer: LCM of 5 and 24 is 120.

2. What are the Factors of 5?

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

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 5 and 24?

Answer:

Least Common Multiple of 5 and 24 = 120

Step 1: Find the prime factorization of 5

5 = 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 5 and 24 is 120.