What is the Least Common Multiple of 39780 and 39800?

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 39780 and 39800 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39780 and 39800, than apply into the LCM equation.

GCF(39780,39800) = 20
LCM(39780,39800) = ( 39780 × 39800) / 20
LCM(39780,39800) = 1583244000 / 20
LCM(39780,39800) = 79162200

Least Common Multiple (LCM) of 39780 and 39800 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 39780 and 39800. First we will calculate the prime factors of 39780 and 39800.

Prime Factorization of 39780

Prime Factorization of 39800

Now multiplying the highest exponent prime factors to calculate the LCM of 39780 and 39800.

LCM(39780,39800) = 2³ × 3² × 5² × 13¹ × 17¹ × 199¹
LCM(39780,39800) = 79162200