What is the Least Common Multiple of 12186 and 12192?

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 12186 and 12192 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12186 and 12192, than apply into the LCM equation.

GCF(12186,12192) = 6
LCM(12186,12192) = ( 12186 × 12192) / 6
LCM(12186,12192) = 148571712 / 6
LCM(12186,12192) = 24761952

Least Common Multiple (LCM) of 12186 and 12192 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12186 and 12192. First we will calculate the prime factors of 12186 and 12192.

Prime Factorization of 12186

Prime Factorization of 12192

Now multiplying the highest exponent prime factors to calculate the LCM of 12186 and 12192.

LCM(12186,12192) = 2⁵ × 3² × 677¹ × 127¹
LCM(12186,12192) = 24761952