Least Common Multiple of 2 and 7

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

• Least Common Multiple of 2 and 7 by Prime method
• Least Common Multiple of 2 and 7 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 2 and 7. First we will calculate the prime factors of 2 and 7.

Prime Factorization of 2

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

2 = 2¹

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 2 and 7.

LCM(2,7) = 2¹×7¹
LCM(2,7) = 14

Factors of 2

List of positive integer factors of 2 that divides 2 without a remainder.

1, 2

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 2 and 7, than apply into the LCM equation.

GCF(2,7) = 1
LCM(2,7) = ( 2 × 7) / 1
LCM(2,7) = 14 / 1
LCM(2,7) = 14

(i) The LCM of 7 and 2 is associative

LCM of 2 and 7 = LCM of 7 and 2

1. What is the LCM of 2 and 7?

Answer: LCM of 2 and 7 is 14.

2. What are the Factors of 2?

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

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 2 and 7?

Answer:

Least Common Multiple of 2 and 7 = 14

Step 1: Find the prime factorization of 2

2 = 2

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 = 14 = 2 x 7

Step 4: Therefore, the least common multiple of 2 and 7 is 14.