What is the Least Common Multiple of 13776 and 13782?

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 13776 and 13782 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13776 and 13782, than apply into the LCM equation.

GCF(13776,13782) = 6
LCM(13776,13782) = ( 13776 × 13782) / 6
LCM(13776,13782) = 189860832 / 6
LCM(13776,13782) = 31643472

Least Common Multiple (LCM) of 13776 and 13782 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13776 and 13782. First we will calculate the prime factors of 13776 and 13782.

Prime Factorization of 13776

Prime Factorization of 13782

Now multiplying the highest exponent prime factors to calculate the LCM of 13776 and 13782.

LCM(13776,13782) = 2⁴ × 3¹ × 7¹ × 41¹ × 2297¹
LCM(13776,13782) = 31643472