Least Common Multiple of 8 and 21

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

• Least Common Multiple of 8 and 21 by Prime method
• Least Common Multiple of 8 and 21 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 21. First we will calculate the prime factors of 8 and 21.

Prime Factorization of 8

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

8 = 2³

Prime Factorization of 21

Prime factors of 21 are 3,7. Prime factorization of 21 in exponential form is:

21 = 3¹×7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 21.

LCM(8,21) = 2³×3¹×7¹
LCM(8,21) = 168

Factors of 8

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

1, 2, 4, 8

Factors of 21

List of positive integer factors of 21 that divides 21 without a remainder.

1, 3, 7, 21

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8 and 21, than apply into the LCM equation.

GCF(8,21) = 1
LCM(8,21) = ( 8 × 21) / 1
LCM(8,21) = 168 / 1
LCM(8,21) = 168

(i) The LCM of 21 and 8 is associative

LCM of 8 and 21 = LCM of 21 and 8

1. What is the LCM of 8 and 21?

Answer: LCM of 8 and 21 is 168.

2. 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.

3. What are the Factors of 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

4. How to Find the LCM of 8 and 21?

Answer:

Least Common Multiple of 8 and 21 = 168

Step 1: Find the prime factorization of 8

8 = 2 x 2 x 2

Step 2: Find the prime factorization of 21

21 = 3 x 7

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

LCM = 168 = 2 x 2 x 2 x 3 x 7

Step 4: Therefore, the least common multiple of 8 and 21 is 168.