What is the Least Common Multiple of 31776 and 31784?

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 31776 and 31784 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31776 and 31784, than apply into the LCM equation.

GCF(31776,31784) = 8
LCM(31776,31784) = ( 31776 × 31784) / 8
LCM(31776,31784) = 1009968384 / 8
LCM(31776,31784) = 126246048

Least Common Multiple (LCM) of 31776 and 31784 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31776 and 31784. First we will calculate the prime factors of 31776 and 31784.

Prime Factorization of 31776

Prime Factorization of 31784

Now multiplying the highest exponent prime factors to calculate the LCM of 31776 and 31784.

LCM(31776,31784) = 2⁵ × 3¹ × 331¹ × 29¹ × 137¹
LCM(31776,31784) = 126246048