What is the Least Common Multiple of 27960 and 27975?

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 of 27960 and 27975 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27960 and 27975, than apply into the LCM equation.

GCF(27960,27975) = 15
LCM(27960,27975) = ( 27960 × 27975) / 15
LCM(27960,27975) = 782181000 / 15
LCM(27960,27975) = 52145400

Least Common Multiple (LCM) of 27960 and 27975 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27960 and 27975. First we will calculate the prime factors of 27960 and 27975.

Prime Factorization of 27960

Prime Factorization of 27975

Now multiplying the highest exponent prime factors to calculate the LCM of 27960 and 27975.

LCM(27960,27975) = 2³ × 3¹ × 5² × 233¹ × 373¹
LCM(27960,27975) = 52145400