Least Common Multiple of 3 and 22

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

• Least Common Multiple of 3 and 22 by Prime method
• Least Common Multiple of 3 and 22 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 22. First we will calculate the prime factors of 3 and 22.

Prime Factorization of 3

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

3 = 3¹

Prime Factorization of 22

Prime factors of 22 are 2,11. Prime factorization of 22 in exponential form is:

22 = 2¹×11¹

Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 22.

LCM(3,22) = 2¹×3¹×11¹
LCM(3,22) = 66

Factors of 3

List of positive integer factors of 3 that divides 3 without a remainder.

1, 3

Factors of 22

List of positive integer factors of 22 that divides 22 without a remainder.

1, 2, 11, 22

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 22, than apply into the LCM equation.

GCF(3,22) = 1
LCM(3,22) = ( 3 × 22) / 1
LCM(3,22) = 66 / 1
LCM(3,22) = 66

(i) The LCM of 22 and 3 is associative

LCM of 3 and 22 = LCM of 22 and 3

1. What is the LCM of 3 and 22?

Answer: LCM of 3 and 22 is 66.

2. What are the Factors of 3?

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

3. What are the Factors of 22?

Answer: Factors of 22 are 1, 2, 11, 22. There are 4 integers that are factors of 22. The greatest factor of 22 is 22.

4. How to Find the LCM of 3 and 22?

Answer:

Least Common Multiple of 3 and 22 = 66

Step 1: Find the prime factorization of 3

3 = 3

Step 2: Find the prime factorization of 22

22 = 2 x 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 3 and 22 is 66.