Least Common Multiple of 30 and 31

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 30 and 31 the smallest integer that is 930 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 31 is 930.

LCM(30,31) = 930

LCM of 30 and 31

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

LCM of:
and

Least Common Multiple of 30 and 31

LCM of 30 and 31 is 930

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 31. First we will calculate the prime factors of 30 and 31.

Prime Factorization of 30


2 30
3 15
5 5
1

Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

Prime Factorization of 31


31 31
1

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 30 and 31.

LCM(30,31) = 21×31×51×311
LCM(30,31) = 930

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30

Factors of 31

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

1, 31

Least Common Multiple of 30 and 31 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30 and 31, than apply into the LCM equation.

GCF(30,31) = 1
LCM(30,31) = ( 30 × 31) / 1
LCM(30,31) = 930 / 1
LCM(30,31) = 930

Properties of LCM 30 and 31

(i) The LCM of 31 and 30 is associative

LCM of 30 and 31 = LCM of 31 and 30

Related Least Common Multiples of 30

Related Least Common Multiples of 31

Frequently Asked Questions on LCM of 30 and 31

1. What is the LCM of 30 and 31?

Answer: LCM of 30 and 31 is 930.

2. What are the Factors of 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

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 30 and 31?

Answer:

Least Common Multiple of 30 and 31 = 930

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

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 = 930 = 2 x 3 x 5 x 31

Step 4: Therefore, the least common multiple of 30 and 31 is 930.