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Least Common Multiple of 36 and 45

Free LCM Calculator determines the least common multiple (LCM) between 36 and 45 the smallest integer that is 180 that is divisible by both numbers.

Least Common Multiple (LCM) of 36 and 45 is 180.

LCM(36,45) = 180

LCM of 36 and 45

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

LCM of:
and

Least Common Multiple (LCM) of 36 and 45 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36 and 45. First we will calculate the prime factors of 36 and 45.

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

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 36 and 45.

LCM(36,45) = 22×32×51
LCM(36,45) = 180

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

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 36 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 36 and 45, than apply into the LCM equation.

GCF(36,45) = 9
LCM(36,45) = ( 36 × 45) / 9
LCM(36,45) = 1620 / 9
LCM(36,45) = 180

Least Common Multiple of 36 and 45 by Listing Multiples

Multiples of 36

36, 72, 108, 144,180

Multiples of 45

45, 90, 135,180

Find the smallest number that is on all of the lists. We have it in bold above.

∴ Least Common Multiple of 36 and 45 is 180

Properties of LCM 36 and 45

(i) The LCM of 45 and 36 is associative

LCM of 36 and 45 = LCM of 45 and 36

Frequently Asked Questions on LCM of 36 and 45

1. What is the LCM of 36 and 45?

Answer: LCM of 36 and 45 is 180.

2. 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.

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 36 and 45?

Answer:

Least Common Multiple of 36 and 45 = 180

Step 1: Find the prime factorization of 36

36 = 2 x 2 x 3 x 3

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 = 180 = 2 x 2 x 3 x 3 x 5

Step 4: Therefore, the least common multiple of 36 and 45 is 180.