What is the Least Common Multiple of 27825 and 27840?

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 27825 and 27840 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27825 and 27840, than apply into the LCM equation.

GCF(27825,27840) = 15
LCM(27825,27840) = ( 27825 × 27840) / 15
LCM(27825,27840) = 774648000 / 15
LCM(27825,27840) = 51643200

Least Common Multiple (LCM) of 27825 and 27840 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27825 and 27840. First we will calculate the prime factors of 27825 and 27840.

Prime Factorization of 27825

Prime Factorization of 27840

Now multiplying the highest exponent prime factors to calculate the LCM of 27825 and 27840.

LCM(27825,27840) = 3¹ × 5² × 7¹ × 53¹ × 2⁶ × 29¹
LCM(27825,27840) = 51643200