Least Common Multiple of 27 and 31

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

• Least Common Multiple of 27 and 31 by Prime method
• Least Common Multiple of 27 and 31 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 27 and 31. First we will calculate the prime factors of 27 and 31.

Prime Factorization of 27

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

27 = 3³

Prime Factorization of 31

Prime factors of 31 are 31. Prime factorization of 31 in exponential form is:

31 = 31¹

Now multiplying the highest exponent prime factors to calculate the LCM of 27 and 31.

LCM(27,31) = 3³×31¹
LCM(27,31) = 837

Factors of 27

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

1, 3, 9, 27

Factors of 31

List of positive integer factors of 31 that divides 31 without a remainder.

1, 31

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27 and 31, than apply into the LCM equation.

GCF(27,31) = 1
LCM(27,31) = ( 27 × 31) / 1
LCM(27,31) = 837 / 1
LCM(27,31) = 837

(i) The LCM of 31 and 27 is associative

LCM of 27 and 31 = LCM of 31 and 27

1. What is the LCM of 27 and 31?

Answer: LCM of 27 and 31 is 837.

2. 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.

3. What are the Factors of 31?

Answer: Factors of 31 are 1, 31. There are 2 integers that are factors of 31. The greatest factor of 31 is 31.

4. How to Find the LCM of 27 and 31?

Answer:

Least Common Multiple of 27 and 31 = 837

Step 1: Find the prime factorization of 27

27 = 3 x 3 x 3

Step 2: Find the prime factorization of 31

31 = 31

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

LCM = 837 = 3 x 3 x 3 x 31

Step 4: Therefore, the least common multiple of 27 and 31 is 837.