What is the Least Common Multiple of 51504 and 51519?

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 51504 and 51519 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51504 and 51519, than apply into the LCM equation.

GCF(51504,51519) = 3
LCM(51504,51519) = ( 51504 × 51519) / 3
LCM(51504,51519) = 2653434576 / 3
LCM(51504,51519) = 884478192

Least Common Multiple (LCM) of 51504 and 51519 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51504 and 51519. First we will calculate the prime factors of 51504 and 51519.

Prime Factorization of 51504

Prime Factorization of 51519

Now multiplying the highest exponent prime factors to calculate the LCM of 51504 and 51519.

LCM(51504,51519) = 2⁴ × 3¹ × 29¹ × 37¹ × 13¹ × 1321¹
LCM(51504,51519) = 884478192