What is the Least Common Multiple of 31890 and 31894?

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 31890 and 31894 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31890 and 31894, than apply into the LCM equation.

GCF(31890,31894) = 2
LCM(31890,31894) = ( 31890 × 31894) / 2
LCM(31890,31894) = 1017099660 / 2
LCM(31890,31894) = 508549830

Least Common Multiple (LCM) of 31890 and 31894 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31890 and 31894. First we will calculate the prime factors of 31890 and 31894.

Prime Factorization of 31890

Prime Factorization of 31894

Now multiplying the highest exponent prime factors to calculate the LCM of 31890 and 31894.

LCM(31890,31894) = 2¹ × 3¹ × 5¹ × 1063¹ × 37¹ × 431¹
LCM(31890,31894) = 508549830