What is the Least Common Multiple of 31776 and 31785?

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 31785 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 31785, than apply into the LCM equation.

GCF(31776,31785) = 3
LCM(31776,31785) = ( 31776 × 31785) / 3
LCM(31776,31785) = 1010000160 / 3
LCM(31776,31785) = 336666720

Least Common Multiple (LCM) of 31776 and 31785 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31776 and 31785. First we will calculate the prime factors of 31776 and 31785.

Prime Factorization of 31776

Prime Factorization of 31785

Now multiplying the highest exponent prime factors to calculate the LCM of 31776 and 31785.

LCM(31776,31785) = 2⁵ × 3¹ × 331¹ × 5¹ × 13¹ × 163¹
LCM(31776,31785) = 336666720