What is the Least Common Multiple of 31284 and 31296?

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 31284 and 31296 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31284 and 31296, than apply into the LCM equation.

GCF(31284,31296) = 12
LCM(31284,31296) = ( 31284 × 31296) / 12
LCM(31284,31296) = 979064064 / 12
LCM(31284,31296) = 81588672

Least Common Multiple (LCM) of 31284 and 31296 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31284 and 31296. First we will calculate the prime factors of 31284 and 31296.

Prime Factorization of 31284

Prime Factorization of 31296

Now multiplying the highest exponent prime factors to calculate the LCM of 31284 and 31296.

LCM(31284,31296) = 2⁶ × 3² × 11¹ × 79¹ × 163¹
LCM(31284,31296) = 81588672