Least Common Multiple of 10 and 11

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

• Least Common Multiple of 10 and 11 by Prime method
• Least Common Multiple of 10 and 11 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 11. First we will calculate the prime factors of 10 and 11.

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 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 10 and 11.

LCM(10,11) = 2¹×5¹×11¹
LCM(10,11) = 110

Factors of 10

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

1, 2, 5, 10

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 10 and 11, than apply into the LCM equation.

GCF(10,11) = 1
LCM(10,11) = ( 10 × 11) / 1
LCM(10,11) = 110 / 1
LCM(10,11) = 110

(i) The LCM of 11 and 10 is associative

LCM of 10 and 11 = LCM of 11 and 10

1. What is the LCM of 10 and 11?

Answer: LCM of 10 and 11 is 110.

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 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 10 and 11?

Answer:

Least Common Multiple of 10 and 11 = 110

Step 1: Find the prime factorization of 10

10 = 2 x 5

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 = 110 = 2 x 5 x 11

Step 4: Therefore, the least common multiple of 10 and 11 is 110.