What is the Least Common Multiple of 30 and 75?
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 30 and 75 is 150.
LCM(30,75) = 150
Least Common Multiple of 30 and 75 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30 and 75, than apply into the LCM equation.
GCF(30,75) = 15
LCM(30,75) = ( 30 × 75) / 15
LCM(30,75) = 2250 / 15
LCM(30,75) = 150
Least Common Multiple (LCM) of 30 and 75 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 75. First we will calculate the prime factors of 30 and 75.
Prime Factorization of 30
Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:
30 = 21 × 31 × 51
Prime Factorization of 75
Prime factors of 75 are 3, 5. Prime factorization of 75 in exponential form is:
75 = 31 × 52
Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 75.
LCM(30,75) = 21 × 31 × 52
LCM(30,75) = 150