What is the Least Common Multiple of 40 and 45?

The least common multiple or lowest common denominators (LCD) can be calculated in two ways; with the LCM formula calculation of the greatest common factor (GCF), or by multiplying the prime factors with the highest exponent factor.

The least common multiple (LCM) of 40 and 45 is 360.

LCM(40,45) = 360

Least Common Multiple of 40 and 45 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate the greatest common factors 40 and 45 and then apply them to the LCM equation.

GCF(40,45) = 5

LCM(40,45) = ( 40 × 45) / 5

LCM(40,45) = 1800 / 5

LCM(40,45) = 360

Least Common Multiple (LCM) of 40 and 45 with Primes

The least common multiple can be found by multiplying the highest exponent prime factors of 40 and 45. 

First, we will calculate the prime factors of 40 and 45.

Prime Factorization of 40

Prime factors of 40 are 2, 5. 

Prime factorization of 40 in exponential form is:

40 = 2³ × 5¹

Prime Factorization of 45

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 40 and 45.

LCM(40,45) = 2³ × 5¹ × 3²

LCM(40,45) = 360