Least Common Multiple of 10 and 8

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

• Least Common Multiple of 10 and 8 by Prime method
• Least Common Multiple of 10 and 8 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 8. First we will calculate the prime factors of 10 and 8.

Prime Factorization of 10

Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:

10 = 2¹×5¹

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 10 and 8.

LCM(10,8) = 2³×5¹
LCM(10,8) = 40

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5, 10

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 10 and 8, than apply into the LCM equation.

GCF(10,8) = 2
LCM(10,8) = ( 10 × 8) / 2
LCM(10,8) = 80 / 2
LCM(10,8) = 40

(i) The LCM of 8 and 10 is associative

LCM of 10 and 8 = LCM of 8 and 10

1. What is the LCM of 10 and 8?

Answer: LCM of 10 and 8 is 40.

2. What are the Factors of 10?

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

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 10 and 8?

Answer:

Least Common Multiple of 10 and 8 = 40

Step 1: Find the prime factorization of 10

10 = 2 x 5

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 = 40 = 2 x 2 x 2 x 5

Step 4: Therefore, the least common multiple of 10 and 8 is 40.