What is the Least Common Multiple of 9999 and 10003?

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 9999 and 10003 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9999 and 10003, than apply into the LCM equation.

GCF(9999,10003) = 1
LCM(9999,10003) = ( 9999 × 10003) / 1
LCM(9999,10003) = 100019997 / 1
LCM(9999,10003) = 100019997

Least Common Multiple (LCM) of 9999 and 10003 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9999 and 10003. First we will calculate the prime factors of 9999 and 10003.

Prime Factorization of 9999

Prime Factorization of 10003

Now multiplying the highest exponent prime factors to calculate the LCM of 9999 and 10003.

LCM(9999,10003) = 3² × 11¹ × 101¹ × 7¹ × 1429¹
LCM(9999,10003) = 100019997