Least Common Multiple of 7 and 8

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

• Least Common Multiple of 7 and 8 by Prime method
• Least Common Multiple of 7 and 8 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 7 and 8. First we will calculate the prime factors of 7 and 8.

Prime Factorization of 7

Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:

7 = 7¹

Prime Factorization of 8

Prime factors of 8 are 2. Prime factorization of 8 in exponential form is:

8 = 2³

Now multiplying the highest exponent prime factors to calculate the LCM of 7 and 8.

LCM(7,8) = 2³×7¹
LCM(7,8) = 56

Factors of 7

List of positive integer factors of 7 that divides 7 without a remainder.

1, 7

Factors of 8

List of positive integer factors of 8 that divides 8 without a remainder.

1, 2, 4, 8

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7 and 8, than apply into the LCM equation.

GCF(7,8) = 1
LCM(7,8) = ( 7 × 8) / 1
LCM(7,8) = 56 / 1
LCM(7,8) = 56

(i) The LCM of 8 and 7 is associative

LCM of 7 and 8 = LCM of 8 and 7

1. What is the LCM of 7 and 8?

Answer: LCM of 7 and 8 is 56.

2. What are the Factors of 7?

Answer: Factors of 7 are 1, 7. There are 2 integers that are factors of 7. The greatest factor of 7 is 7.

3. What are the Factors of 8?

Answer: Factors of 8 are 1, 2, 4, 8. There are 4 integers that are factors of 8. The greatest factor of 8 is 8.

4. How to Find the LCM of 7 and 8?

Answer:

Least Common Multiple of 7 and 8 = 56

Step 1: Find the prime factorization of 7

7 = 7

Step 2: Find the prime factorization of 8

8 = 2 x 2 x 2

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 56 = 2 x 2 x 2 x 7

Step 4: Therefore, the least common multiple of 7 and 8 is 56.