What is the Least Common Multiple of 45504 and 45519?

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 45504 and 45519 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45504 and 45519, than apply into the LCM equation.

GCF(45504,45519) = 3
LCM(45504,45519) = ( 45504 × 45519) / 3
LCM(45504,45519) = 2071296576 / 3
LCM(45504,45519) = 690432192

Least Common Multiple (LCM) of 45504 and 45519 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 45504 and 45519. First we will calculate the prime factors of 45504 and 45519.

Prime Factorization of 45504

Prime Factorization of 45519

Now multiplying the highest exponent prime factors to calculate the LCM of 45504 and 45519.

LCM(45504,45519) = 2⁶ × 3² × 79¹ × 15173¹
LCM(45504,45519) = 690432192