Least Common Multiple of 30 and 32

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 32 the smallest integer that is 480 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 32 is 480.

LCM(30,32) = 480

LCM of 30 and 32

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

LCM of:
and

Least Common Multiple of 30 and 32

LCM of 30 and 32 is 480

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 32. First we will calculate the prime factors of 30 and 32.

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 32


2 32
2 16
2 8
2 4
2 2
1

Prime factors of 32 are 2. Prime factorization of 32 in exponential form is:

32 = 25

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 32.

LCM(30,32) = 25×31×51
LCM(30,32) = 480

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 32

List of positive integer factors of 32 that divides 32 without a remainder.

1, 2, 4, 8, 16, 32

Least Common Multiple of 30 and 32 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 32, than apply into the LCM equation.

GCF(30,32) = 2
LCM(30,32) = ( 30 × 32) / 2
LCM(30,32) = 960 / 2
LCM(30,32) = 480

Properties of LCM 30 and 32

(i) The LCM of 32 and 30 is associative

LCM of 30 and 32 = LCM of 32 and 30

Related Least Common Multiples of 30

Related Least Common Multiples of 32

Frequently Asked Questions on LCM of 30 and 32

1. What is the LCM of 30 and 32?

Answer: LCM of 30 and 32 is 480.

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 32?

Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.

4. How to Find the LCM of 30 and 32?

Answer:

Least Common Multiple of 30 and 32 = 480

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

Step 2: Find the prime factorization of 32

32 = 2 x 2 x 2 x 2 x 2

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

LCM = 480 = 2 x 2 x 2 x 2 x 2 x 3 x 5

Step 4: Therefore, the least common multiple of 30 and 32 is 480.