What is the Least Common Multiple of 19500 and 19505?

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 19500 and 19505 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19500 and 19505, than apply into the LCM equation.

GCF(19500,19505) = 5
LCM(19500,19505) = ( 19500 × 19505) / 5
LCM(19500,19505) = 380347500 / 5
LCM(19500,19505) = 76069500

Least Common Multiple (LCM) of 19500 and 19505 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19500 and 19505. First we will calculate the prime factors of 19500 and 19505.

Prime Factorization of 19500

Prime Factorization of 19505

Now multiplying the highest exponent prime factors to calculate the LCM of 19500 and 19505.

LCM(19500,19505) = 2² × 3¹ × 5³ × 13¹ × 47¹ × 83¹
LCM(19500,19505) = 76069500