What is the Least Common Multiple of 25296 and 25314?

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 25296 and 25314 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25296 and 25314, than apply into the LCM equation.

GCF(25296,25314) = 6
LCM(25296,25314) = ( 25296 × 25314) / 6
LCM(25296,25314) = 640342944 / 6
LCM(25296,25314) = 106723824

Least Common Multiple (LCM) of 25296 and 25314 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 25296 and 25314. First we will calculate the prime factors of 25296 and 25314.

Prime Factorization of 25296

Prime Factorization of 25314

Now multiplying the highest exponent prime factors to calculate the LCM of 25296 and 25314.

LCM(25296,25314) = 2⁴ × 3¹ × 17¹ × 31¹ × 4219¹
LCM(25296,25314) = 106723824