What is the Least Common Multiple of 19776 and 19785?

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 19776 and 19785 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19776 and 19785, than apply into the LCM equation.

GCF(19776,19785) = 3
LCM(19776,19785) = ( 19776 × 19785) / 3
LCM(19776,19785) = 391268160 / 3
LCM(19776,19785) = 130422720

Least Common Multiple (LCM) of 19776 and 19785 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19776 and 19785. First we will calculate the prime factors of 19776 and 19785.

Prime Factorization of 19776

Prime Factorization of 19785

Now multiplying the highest exponent prime factors to calculate the LCM of 19776 and 19785.

LCM(19776,19785) = 2⁶ × 3¹ × 103¹ × 5¹ × 1319¹
LCM(19776,19785) = 130422720