Least Common Multiple of 44 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 44 and 45 the smallest integer that is 1980 that is divisible by both numbers.

Least Common Multiple (LCM) of 44 and 45 is 1980.

LCM(44,45) = 1980

LCM of 44 and 45

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

LCM of:
and

Least Common Multiple of 44 and 45

LCM of 44 and 45 is 1980

Least common multiple can be found by multiplying the highest exponent prime factors of 44 and 45. First we will calculate the prime factors of 44 and 45.

Prime Factorization of 44


2 44
2 22
11 11
1

Prime factors of 44 are 2,11. Prime factorization of 44 in exponential form is:

44 = 22×111

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 44 and 45.

LCM(44,45) = 22×32×51×111
LCM(44,45) = 1980

Factors of 44

List of positive integer factors of 44 that divides 44 without a remainder.

1, 2, 4, 11, 22, 44

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 44 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 44 and 45, than apply into the LCM equation.

GCF(44,45) = 1
LCM(44,45) = ( 44 × 45) / 1
LCM(44,45) = 1980 / 1
LCM(44,45) = 1980

Properties of LCM 44 and 45

(i) The LCM of 45 and 44 is associative

LCM of 44 and 45 = LCM of 45 and 44

Related Least Common Multiples of 44

Related Least Common Multiples of 45

Frequently Asked Questions on LCM of 44 and 45

1. What is the LCM of 44 and 45?

Answer: LCM of 44 and 45 is 1980.

2. What are the Factors of 44?

Answer: Factors of 44 are 1, 2, 4, 11, 22, 44. There are 6 integers that are factors of 44. The greatest factor of 44 is 44.

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 44 and 45?

Answer:

Least Common Multiple of 44 and 45 = 1980

Step 1: Find the prime factorization of 44

44 = 2 x 2 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 = 1980 = 2 x 2 x 3 x 3 x 5 x 11

Step 4: Therefore, the least common multiple of 44 and 45 is 1980.