What is the Least Common Multiple of 39800 and 39805?

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 39800 and 39805 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39800 and 39805, than apply into the LCM equation.

GCF(39800,39805) = 5
LCM(39800,39805) = ( 39800 × 39805) / 5
LCM(39800,39805) = 1584239000 / 5
LCM(39800,39805) = 316847800

Least Common Multiple (LCM) of 39800 and 39805 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39800 and 39805. First we will calculate the prime factors of 39800 and 39805.

Prime Factorization of 39800

Prime Factorization of 39805

Now multiplying the highest exponent prime factors to calculate the LCM of 39800 and 39805.

LCM(39800,39805) = 2³ × 5² × 199¹ × 19¹ × 419¹
LCM(39800,39805) = 316847800