Least Common Multiple of 3 and 20

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

• Least Common Multiple of 3 and 20 by Prime method
• Least Common Multiple of 3 and 20 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 20. First we will calculate the prime factors of 3 and 20.

Prime Factorization of 3

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

3 = 3¹

Prime Factorization of 20

Prime factors of 20 are 2,5. Prime factorization of 20 in exponential form is:

20 = 2²×5¹

Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 20.

LCM(3,20) = 2²×3¹×5¹
LCM(3,20) = 60

Factors of 3

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

1, 3

Factors of 20

List of positive integer factors of 20 that divides 20 without a remainder.

1, 2, 4, 5, 10, 20

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 20, than apply into the LCM equation.

GCF(3,20) = 1
LCM(3,20) = ( 3 × 20) / 1
LCM(3,20) = 60 / 1
LCM(3,20) = 60

(i) The LCM of 20 and 3 is associative

LCM of 3 and 20 = LCM of 20 and 3

1. What is the LCM of 3 and 20?

Answer: LCM of 3 and 20 is 60.

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 20?

Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.

4. How to Find the LCM of 3 and 20?

Answer:

Least Common Multiple of 3 and 20 = 60

Step 1: Find the prime factorization of 3

3 = 3

Step 2: Find the prime factorization of 20

20 = 2 x 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 = 60 = 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 3 and 20 is 60.