What is the Least Common Multiple of 19705 and 19725?

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 19705 and 19725 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19705 and 19725, than apply into the LCM equation.

GCF(19705,19725) = 5
LCM(19705,19725) = ( 19705 × 19725) / 5
LCM(19705,19725) = 388681125 / 5
LCM(19705,19725) = 77736225

Least Common Multiple (LCM) of 19705 and 19725 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19705 and 19725. First we will calculate the prime factors of 19705 and 19725.

Prime Factorization of 19705

Prime Factorization of 19725

Now multiplying the highest exponent prime factors to calculate the LCM of 19705 and 19725.

LCM(19705,19725) = 5² × 7¹ × 563¹ × 3¹ × 263¹
LCM(19705,19725) = 77736225