Least Common Multiple of 33 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 33 and 45 the smallest integer that is 495 that is divisible by both numbers.

Least Common Multiple (LCM) of 33 and 45 is 495.

LCM(33,45) = 495

LCM of 33 and 45

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

LCM of:
and

Least Common Multiple of 33 and 45

LCM of 33 and 45 is 495

Least common multiple can be found by multiplying the highest exponent prime factors of 33 and 45. First we will calculate the prime factors of 33 and 45.

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

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 33 and 45.

LCM(33,45) = 32×51×111
LCM(33,45) = 495

Factors of 33

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

1, 3, 11, 33

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 33 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 33 and 45, than apply into the LCM equation.

GCF(33,45) = 3
LCM(33,45) = ( 33 × 45) / 3
LCM(33,45) = 1485 / 3
LCM(33,45) = 495

Properties of LCM 33 and 45

(i) The LCM of 45 and 33 is associative

LCM of 33 and 45 = LCM of 45 and 33

Related Least Common Multiples of 33

Related Least Common Multiples of 45

Frequently Asked Questions on LCM of 33 and 45

1. What is the LCM of 33 and 45?

Answer: LCM of 33 and 45 is 495.

2. 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.

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 33 and 45?

Answer:

Least Common Multiple of 33 and 45 = 495

Step 1: Find the prime factorization of 33

33 = 3 x 11

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 = 495 = 3 x 3 x 5 x 11

Step 4: Therefore, the least common multiple of 33 and 45 is 495.