What is the Least Common Multiple of 31983 and 31993?

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 31983 and 31993 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31983 and 31993, than apply into the LCM equation.

GCF(31983,31993) = 1
LCM(31983,31993) = ( 31983 × 31993) / 1
LCM(31983,31993) = 1023232119 / 1
LCM(31983,31993) = 1023232119

Least Common Multiple (LCM) of 31983 and 31993 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31983 and 31993. First we will calculate the prime factors of 31983 and 31993.

Prime Factorization of 31983

Prime Factorization of 31993

Now multiplying the highest exponent prime factors to calculate the LCM of 31983 and 31993.

LCM(31983,31993) = 3¹ × 7¹ × 1523¹ × 13¹ × 23¹ × 107¹
LCM(31983,31993) = 1023232119