What is the Least Common Multiple of 31185 and 31194?

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 31185 and 31194 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31185 and 31194, than apply into the LCM equation.

GCF(31185,31194) = 9
LCM(31185,31194) = ( 31185 × 31194) / 9
LCM(31185,31194) = 972784890 / 9
LCM(31185,31194) = 108087210

Least Common Multiple (LCM) of 31185 and 31194 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31185 and 31194. First we will calculate the prime factors of 31185 and 31194.

Prime Factorization of 31185

Prime Factorization of 31194

Now multiplying the highest exponent prime factors to calculate the LCM of 31185 and 31194.

LCM(31185,31194) = 3⁴ × 5¹ × 7¹ × 11¹ × 2¹ × 1733¹
LCM(31185,31194) = 108087210