Least Common Multiple of 32 and 36

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 32 and 36 the smallest integer that is 288 that is divisible by both numbers.

Least Common Multiple (LCM) of 32 and 36 is 288.

LCM(32,36) = 288

LCM of 32 and 36

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

LCM of:
and

Least Common Multiple of 32 and 36

LCM of 32 and 36 is 288

Least common multiple can be found by multiplying the highest exponent prime factors of 32 and 36. First we will calculate the prime factors of 32 and 36.

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

Prime Factorization of 36


2 36
2 18
3 9
3 3
1

Prime factors of 36 are 2,3. Prime factorization of 36 in exponential form is:

36 = 22×32

Now multiplying the highest exponent prime factors to calculate the LCM of 32 and 36.

LCM(32,36) = 25×32
LCM(32,36) = 288

Factors of 32

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

1, 2, 4, 8, 16, 32

Factors of 36

List of positive integer factors of 36 that divides 36 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36

Least Common Multiple of 32 and 36 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32 and 36, than apply into the LCM equation.

GCF(32,36) = 4
LCM(32,36) = ( 32 × 36) / 4
LCM(32,36) = 1152 / 4
LCM(32,36) = 288

Properties of LCM 32 and 36

(i) The LCM of 36 and 32 is associative

LCM of 32 and 36 = LCM of 36 and 32

Related Least Common Multiples of 32

Related Least Common Multiples of 36

Frequently Asked Questions on LCM of 32 and 36

1. What is the LCM of 32 and 36?

Answer: LCM of 32 and 36 is 288.

2. 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.

3. What are the Factors of 36?

Answer: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. There are 9 integers that are factors of 36. The greatest factor of 36 is 36.

4. How to Find the LCM of 32 and 36?

Answer:

Least Common Multiple of 32 and 36 = 288

Step 1: Find the prime factorization of 32

32 = 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 36

36 = 2 x 2 x 3 x 3

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

LCM = 288 = 2 x 2 x 2 x 2 x 2 x 3 x 3

Step 4: Therefore, the least common multiple of 32 and 36 is 288.