What is the Least Common Multiple of 19800 and 19805?

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 19800 and 19805 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19800 and 19805, than apply into the LCM equation.

GCF(19800,19805) = 5
LCM(19800,19805) = ( 19800 × 19805) / 5
LCM(19800,19805) = 392139000 / 5
LCM(19800,19805) = 78427800

Least Common Multiple (LCM) of 19800 and 19805 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19800 and 19805. First we will calculate the prime factors of 19800 and 19805.

Prime Factorization of 19800

Prime Factorization of 19805

Now multiplying the highest exponent prime factors to calculate the LCM of 19800 and 19805.

LCM(19800,19805) = 2³ × 3² × 5² × 11¹ × 17¹ × 233¹
LCM(19800,19805) = 78427800