What is the Least Common Multiple of 75 and 87?
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 87 is 2175.
LCM(75,87) = 2175
Least Common Multiple of 75 and 87 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 87, than apply into the LCM equation.
GCF(75,87) = 3
LCM(75,87) = ( 75 × 87) / 3
LCM(75,87) = 6525 / 3
LCM(75,87) = 2175
Least Common Multiple (LCM) of 75 and 87 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 75 and 87. First we will calculate the prime factors of 75 and 87.
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 87
Prime factors of 87 are 3, 29. Prime factorization of 87 in exponential form is:
87 = 31 × 291
Now multiplying the highest exponent prime factors to calculate the LCM of 75 and 87.
LCM(75,87) = 31 × 52 × 291
LCM(75,87) = 2175