What is the Least Common Multiple of 75 and 83?
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 83 is 6225.
LCM(75,83) = 6225
Least Common Multiple of 75 and 83 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 83, than apply into the LCM equation.
GCF(75,83) = 1
LCM(75,83) = ( 75 × 83) / 1
LCM(75,83) = 6225 / 1
LCM(75,83) = 6225
Least Common Multiple (LCM) of 75 and 83 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 75 and 83. First we will calculate the prime factors of 75 and 83.
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 83
Prime factors of 83 are 83. Prime factorization of 83 in exponential form is:
83 = 831
Now multiplying the highest exponent prime factors to calculate the LCM of 75 and 83.
LCM(75,83) = 31 × 52 × 831
LCM(75,83) = 6225