Least Common Multiple of 31 and 3

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

• Least Common Multiple of 31 and 3 by Prime method
• Least Common Multiple of 31 and 3 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31 and 3. First we will calculate the prime factors of 31 and 3.

Prime Factorization of 31

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

31 = 31¹

Prime Factorization of 3

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

3 = 3¹

Now multiplying the highest exponent prime factors to calculate the LCM of 31 and 3.

LCM(31,3) = 3¹×31¹
LCM(31,3) = 93

Factors of 31

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

1, 31

Factors of 3

List of positive integer factors of 3 that divides 3 without a remainder.

1, 3

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31 and 3, than apply into the LCM equation.

GCF(31,3) = 1
LCM(31,3) = ( 31 × 3) / 1
LCM(31,3) = 93 / 1
LCM(31,3) = 93

(i) The LCM of 3 and 31 is associative

LCM of 31 and 3 = LCM of 3 and 31

1. What is the LCM of 31 and 3?

Answer: LCM of 31 and 3 is 93.

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 3?

Answer: Factors of 3 are 1, 3. There are 2 integers that are factors of 3. The greatest factor of 3 is 3.

4. How to Find the LCM of 31 and 3?

Answer:

Least Common Multiple of 31 and 3 = 93

Step 1: Find the prime factorization of 31

31 = 31

Step 2: Find the prime factorization of 3

3 = 3

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

LCM = 93 = 3 x 31

Step 4: Therefore, the least common multiple of 31 and 3 is 93.