What is the Least Common Multiple of 31350 and 31365?

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 31350 and 31365 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31350 and 31365, than apply into the LCM equation.

GCF(31350,31365) = 15
LCM(31350,31365) = ( 31350 × 31365) / 15
LCM(31350,31365) = 983292750 / 15
LCM(31350,31365) = 65552850

Least Common Multiple (LCM) of 31350 and 31365 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31350 and 31365. First we will calculate the prime factors of 31350 and 31365.

Prime Factorization of 31350

Prime Factorization of 31365

Now multiplying the highest exponent prime factors to calculate the LCM of 31350 and 31365.

LCM(31350,31365) = 2¹ × 3² × 5² × 11¹ × 19¹ × 17¹ × 41¹
LCM(31350,31365) = 65552850