Least Common Multiple of 45 and 61

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 61 the smallest integer that is 2745 that is divisible by both numbers.

Least Common Multiple (LCM) of 45 and 61 is 2745.

LCM(45,61) = 2745

LCM of 45 and 61

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

LCM of:
and

Least Common Multiple of 45 and 61

LCM of 45 and 61 is 2745

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 61. First we will calculate the prime factors of 45 and 61.

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 61


61 61
1

Prime factors of 61 are 61. Prime factorization of 61 in exponential form is:

61 = 611

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 61.

LCM(45,61) = 32×51×611
LCM(45,61) = 2745

Factors of 45

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

1, 3, 5, 9, 15, 45

Factors of 61

List of positive integer factors of 61 that divides 61 without a remainder.

1, 61

Least Common Multiple of 45 and 61 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 61, than apply into the LCM equation.

GCF(45,61) = 1
LCM(45,61) = ( 45 × 61) / 1
LCM(45,61) = 2745 / 1
LCM(45,61) = 2745

Properties of LCM 45 and 61

(i) The LCM of 61 and 45 is associative

LCM of 45 and 61 = LCM of 61 and 45

Related Least Common Multiples of 45

Related Least Common Multiples of 61

Frequently Asked Questions on LCM of 45 and 61

1. What is the LCM of 45 and 61?

Answer: LCM of 45 and 61 is 2745.

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 61?

Answer: Factors of 61 are 1, 61. There are 2 integers that are factors of 61. The greatest factor of 61 is 61.

4. How to Find the LCM of 45 and 61?

Answer:

Least Common Multiple of 45 and 61 = 2745

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 61

61 = 61

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

LCM = 2745 = 3 x 3 x 5 x 61

Step 4: Therefore, the least common multiple of 45 and 61 is 2745.