What is the Least Common Multiple of 19704 and 19710?

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 19704 and 19710 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19704 and 19710, than apply into the LCM equation.

GCF(19704,19710) = 6
LCM(19704,19710) = ( 19704 × 19710) / 6
LCM(19704,19710) = 388365840 / 6
LCM(19704,19710) = 64727640

Least Common Multiple (LCM) of 19704 and 19710 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19704 and 19710. First we will calculate the prime factors of 19704 and 19710.

Prime Factorization of 19704

Prime Factorization of 19710

Now multiplying the highest exponent prime factors to calculate the LCM of 19704 and 19710.

LCM(19704,19710) = 2³ × 3³ × 821¹ × 5¹ × 73¹
LCM(19704,19710) = 64727640