Least Common Multiple of 31 and 38

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

• Least Common Multiple of 31 and 38 by Prime method
• Least Common Multiple of 31 and 38 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31 and 38. First we will calculate the prime factors of 31 and 38.

Prime Factorization of 31

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

31 = 31¹

Prime Factorization of 38

Prime factors of 38 are 2,19. Prime factorization of 38 in exponential form is:

38 = 2¹×19¹

Now multiplying the highest exponent prime factors to calculate the LCM of 31 and 38.

LCM(31,38) = 2¹×19¹×31¹
LCM(31,38) = 1178

Factors of 31

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

1, 31

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1, 2, 19, 38

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31 and 38, than apply into the LCM equation.

GCF(31,38) = 1
LCM(31,38) = ( 31 × 38) / 1
LCM(31,38) = 1178 / 1
LCM(31,38) = 1178

(i) The LCM of 38 and 31 is associative

LCM of 31 and 38 = LCM of 38 and 31

1. What is the LCM of 31 and 38?

Answer: LCM of 31 and 38 is 1178.

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 38?

Answer: Factors of 38 are 1, 2, 19, 38. There are 4 integers that are factors of 38. The greatest factor of 38 is 38.

4. How to Find the LCM of 31 and 38?

Answer:

Least Common Multiple of 31 and 38 = 1178

Step 1: Find the prime factorization of 31

31 = 31

Step 2: Find the prime factorization of 38

38 = 2 x 19

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

LCM = 1178 = 2 x 19 x 31

Step 4: Therefore, the least common multiple of 31 and 38 is 1178.