Least Common Multiple of 5 and 10

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

• Least Common Multiple of 5 and 10 by Prime method
• Least Common Multiple of 5 and 10 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 10. First we will calculate the prime factors of 5 and 10.

Prime Factorization of 5

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

5 = 5¹

Prime Factorization of 10

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

10 = 2¹×5¹

Now multiplying the highest exponent prime factors to calculate the LCM of 5 and 10.

LCM(5,10) = 2¹×5¹
LCM(5,10) = 10

Factors of 5

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

1, 5

Factors of 10

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

1, 2, 5, 10

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5 and 10, than apply into the LCM equation.

GCF(5,10) = 5
LCM(5,10) = ( 5 × 10) / 5
LCM(5,10) = 50 / 5
LCM(5,10) = 10

(i) The LCM of 10 and 5 is associative

LCM of 5 and 10 = LCM of 10 and 5

1. What is the LCM of 5 and 10?

Answer: LCM of 5 and 10 is 10.

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 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.

4. How to Find the LCM of 5 and 10?

Answer:

Least Common Multiple of 5 and 10 = 10

Step 1: Find the prime factorization of 5

5 = 5

Step 2: Find the prime factorization of 10

10 = 2 x 5

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

LCM = 10 = 2 x 5

Step 4: Therefore, the least common multiple of 5 and 10 is 10.