Least Common Multiple of 45 and 46

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 46 the smallest integer that is 2070 that is divisible by both numbers.

Least Common Multiple (LCM) of 45 and 46 is 2070.

LCM(45,46) = 2070

LCM of 45 and 46

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

LCM of:
and

Least Common Multiple of 45 and 46

LCM of 45 and 46 is 2070

Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 46. First we will calculate the prime factors of 45 and 46.

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 46


2 46
23 23
1

Prime factors of 46 are 2,23. Prime factorization of 46 in exponential form is:

46 = 21×231

Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 46.

LCM(45,46) = 21×32×51×231
LCM(45,46) = 2070

Factors of 45

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

1, 3, 5, 9, 15, 45

Factors of 46

List of positive integer factors of 46 that divides 46 without a remainder.

1, 2, 23, 46

Least Common Multiple of 45 and 46 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 46, than apply into the LCM equation.

GCF(45,46) = 1
LCM(45,46) = ( 45 × 46) / 1
LCM(45,46) = 2070 / 1
LCM(45,46) = 2070

Properties of LCM 45 and 46

(i) The LCM of 46 and 45 is associative

LCM of 45 and 46 = LCM of 46 and 45

Related Least Common Multiples of 45

Related Least Common Multiples of 46

Frequently Asked Questions on LCM of 45 and 46

1. What is the LCM of 45 and 46?

Answer: LCM of 45 and 46 is 2070.

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 46?

Answer: Factors of 46 are 1, 2, 23, 46. There are 4 integers that are factors of 46. The greatest factor of 46 is 46.

4. How to Find the LCM of 45 and 46?

Answer:

Least Common Multiple of 45 and 46 = 2070

Step 1: Find the prime factorization of 45

45 = 3 x 3 x 5

Step 2: Find the prime factorization of 46

46 = 2 x 23

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

LCM = 2070 = 2 x 3 x 3 x 5 x 23

Step 4: Therefore, the least common multiple of 45 and 46 is 2070.