Least Common Multiple of 3 and 7

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

• Least Common Multiple of 3 and 7 by Prime method
• Least Common Multiple of 3 and 7 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 7. First we will calculate the prime factors of 3 and 7.

Prime Factorization of 3

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

3 = 3¹

Prime Factorization of 7

Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:

7 = 7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 7.

LCM(3,7) = 3¹×7¹
LCM(3,7) = 21

Factors of 3

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

1, 3

Factors of 7

List of positive integer factors of 7 that divides 7 without a remainder.

1, 7

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 7, than apply into the LCM equation.

GCF(3,7) = 1
LCM(3,7) = ( 3 × 7) / 1
LCM(3,7) = 21 / 1
LCM(3,7) = 21

(i) The LCM of 7 and 3 is associative

LCM of 3 and 7 = LCM of 7 and 3

1. What is the LCM of 3 and 7?

Answer: LCM of 3 and 7 is 21.

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 7?

Answer: Factors of 7 are 1, 7. There are 2 integers that are factors of 7. The greatest factor of 7 is 7.

4. How to Find the LCM of 3 and 7?

Answer:

Least Common Multiple of 3 and 7 = 21

Step 1: Find the prime factorization of 3

3 = 3

Step 2: Find the prime factorization of 7

7 = 7

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

LCM = 21 = 3 x 7

Step 4: Therefore, the least common multiple of 3 and 7 is 21.