Least Common Multiple of 5 and 6

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

• Least Common Multiple of 5 and 6 by Prime method
• Least Common Multiple of 5 and 6 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 5 and 6. First we will calculate the prime factors of 5 and 6.

Prime Factorization of 5

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

5 = 5¹

Prime Factorization of 6

Prime factors of 6 are 2,3. Prime factorization of 6 in exponential form is:

6 = 2¹×3¹

Now multiplying the highest exponent prime factors to calculate the LCM of 5 and 6.

LCM(5,6) = 2¹×3¹×5¹
LCM(5,6) = 30

Factors of 5

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

1, 5

Factors of 6

List of positive integer factors of 6 that divides 6 without a remainder.

1, 2, 3, 6

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5 and 6, than apply into the LCM equation.

GCF(5,6) = 1
LCM(5,6) = ( 5 × 6) / 1
LCM(5,6) = 30 / 1
LCM(5,6) = 30

(i) The LCM of 6 and 5 is associative

LCM of 5 and 6 = LCM of 6 and 5

1. What is the LCM of 5 and 6?

Answer: LCM of 5 and 6 is 30.

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 6?

Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.

4. How to Find the LCM of 5 and 6?

Answer:

Least Common Multiple of 5 and 6 = 30

Step 1: Find the prime factorization of 5

5 = 5

Step 2: Find the prime factorization of 6

6 = 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 = 30 = 2 x 3 x 5

Step 4: Therefore, the least common multiple of 5 and 6 is 30.