What is the Least Common Multiple of 31296 and 31305?

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 31296 and 31305 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31296 and 31305, than apply into the LCM equation.

GCF(31296,31305) = 3
LCM(31296,31305) = ( 31296 × 31305) / 3
LCM(31296,31305) = 979721280 / 3
LCM(31296,31305) = 326573760

Least Common Multiple (LCM) of 31296 and 31305 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31296 and 31305. First we will calculate the prime factors of 31296 and 31305.

Prime Factorization of 31296

Prime Factorization of 31305

Now multiplying the highest exponent prime factors to calculate the LCM of 31296 and 31305.

LCM(31296,31305) = 2⁶ × 3¹ × 163¹ × 5¹ × 2087¹
LCM(31296,31305) = 326573760