What is the Least Common Multiple of 89904 and 89919?

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 89904 and 89919 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 89904 and 89919, than apply into the LCM equation.

GCF(89904,89919) = 3
LCM(89904,89919) = ( 89904 × 89919) / 3
LCM(89904,89919) = 8084077776 / 3
LCM(89904,89919) = 2694692592

Least Common Multiple (LCM) of 89904 and 89919 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 89904 and 89919. First we will calculate the prime factors of 89904 and 89919.

Prime Factorization of 89904

Prime Factorization of 89919

Now multiplying the highest exponent prime factors to calculate the LCM of 89904 and 89919.

LCM(89904,89919) = 2⁴ × 3² × 1873¹ × 97¹ × 103¹
LCM(89904,89919) = 2694692592