Least Common Multiple of 6 and 11

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

• Least Common Multiple of 6 and 11 by Prime method
• Least Common Multiple of 6 and 11 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 6 and 11. First we will calculate the prime factors of 6 and 11.

Prime Factorization of 6

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

6 = 2¹×3¹

Prime Factorization of 11

Prime factors of 11 are 11. Prime factorization of 11 in exponential form is:

11 = 11¹

Now multiplying the highest exponent prime factors to calculate the LCM of 6 and 11.

LCM(6,11) = 2¹×3¹×11¹
LCM(6,11) = 66

Factors of 6

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

1, 2, 3, 6

Factors of 11

List of positive integer factors of 11 that divides 11 without a remainder.

1, 11

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 6 and 11, than apply into the LCM equation.

GCF(6,11) = 1
LCM(6,11) = ( 6 × 11) / 1
LCM(6,11) = 66 / 1
LCM(6,11) = 66

(i) The LCM of 11 and 6 is associative

LCM of 6 and 11 = LCM of 11 and 6

1. What is the LCM of 6 and 11?

Answer: LCM of 6 and 11 is 66.

2. 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.

3. What are the Factors of 11?

Answer: Factors of 11 are 1, 11. There are 2 integers that are factors of 11. The greatest factor of 11 is 11.

4. How to Find the LCM of 6 and 11?

Answer:

Least Common Multiple of 6 and 11 = 66

Step 1: Find the prime factorization of 6

6 = 2 x 3

Step 2: Find the prime factorization of 11

11 = 11

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

LCM = 66 = 2 x 3 x 11

Step 4: Therefore, the least common multiple of 6 and 11 is 66.