Least Common Multiple of 45 and 58

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 58 the smallest integer that is 2610 that is divisible by both numbers.

Least Common Multiple (LCM) of 45 and 58 is 2610.

LCM(45,58) = 2610

LCM of 45 and 58

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

LCM of:
and

Least Common Multiple of 45 and 58

LCM of 45 and 58 is 2610

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 58. First we will calculate the prime factors of 45 and 58.

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 58


2 58
29 29
1

Prime factors of 58 are 2,29. Prime factorization of 58 in exponential form is:

58 = 21×291

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 58.

LCM(45,58) = 21×32×51×291
LCM(45,58) = 2610

Factors of 45

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

1, 3, 5, 9, 15, 45

Factors of 58

List of positive integer factors of 58 that divides 58 without a remainder.

1, 2, 29, 58

Least Common Multiple of 45 and 58 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 58, than apply into the LCM equation.

GCF(45,58) = 1
LCM(45,58) = ( 45 × 58) / 1
LCM(45,58) = 2610 / 1
LCM(45,58) = 2610

Properties of LCM 45 and 58

(i) The LCM of 58 and 45 is associative

LCM of 45 and 58 = LCM of 58 and 45

Related Least Common Multiples of 45

Related Least Common Multiples of 58

Frequently Asked Questions on LCM of 45 and 58

1. What is the LCM of 45 and 58?

Answer: LCM of 45 and 58 is 2610.

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 58?

Answer: Factors of 58 are 1, 2, 29, 58. There are 4 integers that are factors of 58. The greatest factor of 58 is 58.

4. How to Find the LCM of 45 and 58?

Answer:

Least Common Multiple of 45 and 58 = 2610

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 58

58 = 2 x 29

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

LCM = 2610 = 2 x 3 x 3 x 5 x 29

Step 4: Therefore, the least common multiple of 45 and 58 is 2610.