Least Common Multiple of 7 and 12

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

• Least Common Multiple of 7 and 12 by Prime method
• Least Common Multiple of 7 and 12 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 7 and 12. First we will calculate the prime factors of 7 and 12.

Prime Factorization of 7

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

7 = 7¹

Prime Factorization of 12

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 2²×3¹

Now multiplying the highest exponent prime factors to calculate the LCM of 7 and 12.

LCM(7,12) = 2²×3¹×7¹
LCM(7,12) = 84

Factors of 7

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

1, 7

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7 and 12, than apply into the LCM equation.

GCF(7,12) = 1
LCM(7,12) = ( 7 × 12) / 1
LCM(7,12) = 84 / 1
LCM(7,12) = 84

(i) The LCM of 12 and 7 is associative

LCM of 7 and 12 = LCM of 12 and 7

1. What is the LCM of 7 and 12?

Answer: LCM of 7 and 12 is 84.

2. 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.

3. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

4. How to Find the LCM of 7 and 12?

Answer:

Least Common Multiple of 7 and 12 = 84

Step 1: Find the prime factorization of 7

7 = 7

Step 2: Find the prime factorization of 12

12 = 2 x 2 x 3

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

LCM = 84 = 2 x 2 x 3 x 7

Step 4: Therefore, the least common multiple of 7 and 12 is 84.