What is the Least Common Multiple of 45 and 60?
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 45 and 60 is 180.
LCM(45,60) = 180
Least Common Multiple of 45 and 60 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 60, than apply into the LCM equation.
GCF(45,60) = 15
LCM(45,60) = ( 45 × 60) / 15
LCM(45,60) = 2700 / 15
LCM(45,60) = 180
Least Common Multiple (LCM) of 45 and 60 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 45 and 60. First we will calculate the prime factors of 45 and 60.
Prime Factorization of 45
Prime factors of 45 are 3, 5. Prime factorization of 45 in exponential form is:
45 = 32 × 51
Prime Factorization of 60
Prime factors of 60 are 2, 3, 5. Prime factorization of 60 in exponential form is:
60 = 22 × 31 × 51
Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 60.
LCM(45,60) = 32 × 51 × 22
LCM(45,60) = 180