What is the Least Common Multiple of 40 and 45?
Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.
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 greatest common factor 40 and 45, than apply into 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
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