Least Common Multiple of 30 and 33

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 33 the smallest integer that is 330 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 33 is 330.

LCM(30,33) = 330

LCM of 30 and 33

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

LCM of:
and

Least Common Multiple of 30 and 33

LCM of 30 and 33 is 330

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 33. First we will calculate the prime factors of 30 and 33.

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 33


3 33
11 11
1

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 30 and 33.

LCM(30,33) = 21×31×51×111
LCM(30,33) = 330

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 33

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

1, 3, 11, 33

Least Common Multiple of 30 and 33 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 33, than apply into the LCM equation.

GCF(30,33) = 3
LCM(30,33) = ( 30 × 33) / 3
LCM(30,33) = 990 / 3
LCM(30,33) = 330

Properties of LCM 30 and 33

(i) The LCM of 33 and 30 is associative

LCM of 30 and 33 = LCM of 33 and 30

Related Least Common Multiples of 30

Related Least Common Multiples of 33

Frequently Asked Questions on LCM of 30 and 33

1. What is the LCM of 30 and 33?

Answer: LCM of 30 and 33 is 330.

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 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 30 and 33?

Answer:

Least Common Multiple of 30 and 33 = 330

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

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 = 330 = 2 x 3 x 5 x 11

Step 4: Therefore, the least common multiple of 30 and 33 is 330.