What is the Least Common Multiple of 31997 and 32003?

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 31997 and 32003 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31997 and 32003, than apply into the LCM equation.

GCF(31997,32003) = 1
LCM(31997,32003) = ( 31997 × 32003) / 1
LCM(31997,32003) = 1023999991 / 1
LCM(31997,32003) = 1023999991

Least Common Multiple (LCM) of 31997 and 32003 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31997 and 32003. First we will calculate the prime factors of 31997 and 32003.

Prime Factorization of 31997

Prime Factorization of 32003

Now multiplying the highest exponent prime factors to calculate the LCM of 31997 and 32003.

LCM(31997,32003) = 7² × 653¹ × 32003¹
LCM(31997,32003) = 1023999991