What is the Least Common Multiple of 27945 and 27960?

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 27945 and 27960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27945 and 27960, than apply into the LCM equation.

GCF(27945,27960) = 15
LCM(27945,27960) = ( 27945 × 27960) / 15
LCM(27945,27960) = 781342200 / 15
LCM(27945,27960) = 52089480

Least Common Multiple (LCM) of 27945 and 27960 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27945 and 27960. First we will calculate the prime factors of 27945 and 27960.

Prime Factorization of 27945

Prime Factorization of 27960

Now multiplying the highest exponent prime factors to calculate the LCM of 27945 and 27960.

LCM(27945,27960) = 3⁵ × 5¹ × 23¹ × 2³ × 233¹
LCM(27945,27960) = 52089480