Least Common Multiple of 45 and 55

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 45 and 55 the smallest integer that is 495 that is divisible by both numbers.

Least Common Multiple (LCM) of 45 and 55 is 495.

LCM(45,55) = 495

LCM of 45 and 55

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

LCM of:
and

Least Common Multiple of 45 and 55

LCM of 45 and 55 is 495

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 55. First we will calculate the prime factors of 45 and 55.

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

Prime Factorization of 55


5 55
11 11
1

Prime factors of 55 are 5,11. Prime factorization of 55 in exponential form is:

55 = 51×111

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 55.

LCM(45,55) = 32×51×111
LCM(45,55) = 495

Factors of 45

List of positive integer factors of 45 that divides 45 without a remainder.

1, 3, 5, 9, 15, 45

Factors of 55

List of positive integer factors of 55 that divides 55 without a remainder.

1, 5, 11, 55

Least Common Multiple of 45 and 55 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45 and 55, than apply into the LCM equation.

GCF(45,55) = 5
LCM(45,55) = ( 45 × 55) / 5
LCM(45,55) = 2475 / 5
LCM(45,55) = 495

Properties of LCM 45 and 55

(i) The LCM of 55 and 45 is associative

LCM of 45 and 55 = LCM of 55 and 45

Related Least Common Multiples of 45

Related Least Common Multiples of 55

Frequently Asked Questions on LCM of 45 and 55

1. What is the LCM of 45 and 55?

Answer: LCM of 45 and 55 is 495.

2. 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.

3. What are the Factors of 55?

Answer: Factors of 55 are 1, 5, 11, 55. There are 4 integers that are factors of 55. The greatest factor of 55 is 55.

4. How to Find the LCM of 45 and 55?

Answer:

Least Common Multiple of 45 and 55 = 495

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 55

55 = 5 x 11

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 45 and 55 is 495.