What is the Least Common Multiple of 75 and 90?
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 75 and 90 is 450.
LCM(75,90) = 450
Least Common Multiple of 75 and 90 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75 and 90, than apply into the LCM equation.
GCF(75,90) = 15
LCM(75,90) = ( 75 × 90) / 15
LCM(75,90) = 6750 / 15
LCM(75,90) = 450
Least Common Multiple (LCM) of 75 and 90 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 75 and 90. First we will calculate the prime factors of 75 and 90.
Prime Factorization of 75
Prime factors of 75 are 3, 5. Prime factorization of 75 in exponential form is:
75 = 31 × 52
Prime Factorization of 90
Prime factors of 90 are 2, 3, 5. Prime factorization of 90 in exponential form is:
90 = 21 × 32 × 51
Now multiplying the highest exponent prime factors to calculate the LCM of 75 and 90.
LCM(75,90) = 32 × 52 × 21
LCM(75,90) = 450