What is the Least Common Multiple of 19680 and 19692?

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 19680 and 19692 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19680 and 19692, than apply into the LCM equation.

GCF(19680,19692) = 12
LCM(19680,19692) = ( 19680 × 19692) / 12
LCM(19680,19692) = 387538560 / 12
LCM(19680,19692) = 32294880

Least Common Multiple (LCM) of 19680 and 19692 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19680 and 19692. First we will calculate the prime factors of 19680 and 19692.

Prime Factorization of 19680

Prime Factorization of 19692

Now multiplying the highest exponent prime factors to calculate the LCM of 19680 and 19692.

LCM(19680,19692) = 2⁵ × 3² × 5¹ × 41¹ × 547¹
LCM(19680,19692) = 32294880