Least Common Multiple of 31 and 33

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

• Least Common Multiple of 31 and 33 by Prime method
• Least Common Multiple of 31 and 33 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31 and 33. First we will calculate the prime factors of 31 and 33.

Prime Factorization of 31

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

31 = 31¹

Prime Factorization of 33

Prime factors of 33 are 3,11. Prime factorization of 33 in exponential form is:

33 = 3¹×11¹

Now multiplying the highest exponent prime factors to calculate the LCM of 31 and 33.

LCM(31,33) = 3¹×11¹×31¹
LCM(31,33) = 1023

Factors of 31

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

1, 31

Factors of 33

List of positive integer factors of 33 that divides 33 without a remainder.

1, 3, 11, 33

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31 and 33, than apply into the LCM equation.

GCF(31,33) = 1
LCM(31,33) = ( 31 × 33) / 1
LCM(31,33) = 1023 / 1
LCM(31,33) = 1023

(i) The LCM of 33 and 31 is associative

LCM of 31 and 33 = LCM of 33 and 31

1. What is the LCM of 31 and 33?

Answer: LCM of 31 and 33 is 1023.

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 33?

Answer: Factors of 33 are 1, 3, 11, 33. There are 4 integers that are factors of 33. The greatest factor of 33 is 33.

4. How to Find the LCM of 31 and 33?

Answer:

Least Common Multiple of 31 and 33 = 1023

Step 1: Find the prime factorization of 31

31 = 31

Step 2: Find the prime factorization of 33

33 = 3 x 11

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

LCM = 1023 = 3 x 11 x 31

Step 4: Therefore, the least common multiple of 31 and 33 is 1023.