What is the Least Common Multiple of 81900 and 81909?

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 81900 and 81909 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 81900 and 81909, than apply into the LCM equation.

GCF(81900,81909) = 9
LCM(81900,81909) = ( 81900 × 81909) / 9
LCM(81900,81909) = 6708347100 / 9
LCM(81900,81909) = 745371900

Least Common Multiple (LCM) of 81900 and 81909 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 81900 and 81909. First we will calculate the prime factors of 81900 and 81909.

Prime Factorization of 81900

Prime Factorization of 81909

Now multiplying the highest exponent prime factors to calculate the LCM of 81900 and 81909.

LCM(81900,81909) = 2² × 3² × 5² × 7¹ × 13¹ × 19¹ × 479¹
LCM(81900,81909) = 745371900