Least Common Multiple of 31 and 39

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

• Least Common Multiple of 31 and 39 by Prime method
• Least Common Multiple of 31 and 39 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31 and 39. First we will calculate the prime factors of 31 and 39.

Prime Factorization of 31

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

31 = 31¹

Prime Factorization of 39

Prime factors of 39 are 3,13. Prime factorization of 39 in exponential form is:

39 = 3¹×13¹

Now multiplying the highest exponent prime factors to calculate the LCM of 31 and 39.

LCM(31,39) = 3¹×13¹×31¹
LCM(31,39) = 1209

Factors of 31

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

1, 31

Factors of 39

List of positive integer factors of 39 that divides 39 without a remainder.

1, 3, 13, 39

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31 and 39, than apply into the LCM equation.

GCF(31,39) = 1
LCM(31,39) = ( 31 × 39) / 1
LCM(31,39) = 1209 / 1
LCM(31,39) = 1209

(i) The LCM of 39 and 31 is associative

LCM of 31 and 39 = LCM of 39 and 31

1. What is the LCM of 31 and 39?

Answer: LCM of 31 and 39 is 1209.

2. 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.

3. What are the Factors of 39?

Answer: Factors of 39 are 1, 3, 13, 39. There are 4 integers that are factors of 39. The greatest factor of 39 is 39.

4. How to Find the LCM of 31 and 39?

Answer:

Least Common Multiple of 31 and 39 = 1209

Step 1: Find the prime factorization of 31

31 = 31

Step 2: Find the prime factorization of 39

39 = 3 x 13

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

LCM = 1209 = 3 x 13 x 31

Step 4: Therefore, the least common multiple of 31 and 39 is 1209.