Least Common Multiple of 7 and 27

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

• Least Common Multiple of 7 and 27 by Prime method
• Least Common Multiple of 7 and 27 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 7 and 27. First we will calculate the prime factors of 7 and 27.

Prime Factorization of 7

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

7 = 7¹

Prime Factorization of 27

Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:

27 = 3³

Now multiplying the highest exponent prime factors to calculate the LCM of 7 and 27.

LCM(7,27) = 3³×7¹
LCM(7,27) = 189

Factors of 7

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

1, 7

Factors of 27

List of positive integer factors of 27 that divides 27 without a remainder.

1, 3, 9, 27

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7 and 27, than apply into the LCM equation.

GCF(7,27) = 1
LCM(7,27) = ( 7 × 27) / 1
LCM(7,27) = 189 / 1
LCM(7,27) = 189

(i) The LCM of 27 and 7 is associative

LCM of 7 and 27 = LCM of 27 and 7

1. What is the LCM of 7 and 27?

Answer: LCM of 7 and 27 is 189.

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 27?

Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.

4. How to Find the LCM of 7 and 27?

Answer:

Least Common Multiple of 7 and 27 = 189

Step 1: Find the prime factorization of 7

7 = 7

Step 2: Find the prime factorization of 27

27 = 3 x 3 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 = 189 = 3 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 7 and 27 is 189.