Least Common Multiple of 30 and 45

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 45 the smallest integer that is 90 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 45 is 90.

LCM(30,45) = 90

LCM of 30 and 45

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

LCM of:
and

Least Common Multiple of 30 and 45

LCM of 30 and 45 is 90

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 45. First we will calculate the prime factors of 30 and 45.

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 45


3 45
3 15
5 5
1

Prime factors of 45 are 3,5. Prime factorization of 45 in exponential form is:

45 = 32×51

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 45.

LCM(30,45) = 21×32×51
LCM(30,45) = 90

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 45

List of positive integer factors of 45 that divides 45 without a remainder.

1, 3, 5, 9, 15, 45

Least Common Multiple of 30 and 45 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 45, than apply into the LCM equation.

GCF(30,45) = 15
LCM(30,45) = ( 30 × 45) / 15
LCM(30,45) = 1350 / 15
LCM(30,45) = 90

Properties of LCM 30 and 45

(i) The LCM of 45 and 30 is associative

LCM of 30 and 45 = LCM of 45 and 30

Related Least Common Multiples of 30

Related Least Common Multiples of 45

Frequently Asked Questions on LCM of 30 and 45

1. What is the LCM of 30 and 45?

Answer: LCM of 30 and 45 is 90.

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 45?

Answer: Factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 integers that are factors of 45. The greatest factor of 45 is 45.

4. How to Find the LCM of 30 and 45?

Answer:

Least Common Multiple of 30 and 45 = 90

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 45

45 = 3 x 3 x 5

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

LCM = 90 = 2 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 30 and 45 is 90.