What is the Least Common Multiple of 78288 and 78304?

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 78288 and 78304 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78288 and 78304, than apply into the LCM equation.

GCF(78288,78304) = 16
LCM(78288,78304) = ( 78288 × 78304) / 16
LCM(78288,78304) = 6130263552 / 16
LCM(78288,78304) = 383141472

Least Common Multiple (LCM) of 78288 and 78304 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78288 and 78304. First we will calculate the prime factors of 78288 and 78304.

Prime Factorization of 78288

Prime Factorization of 78304

Now multiplying the highest exponent prime factors to calculate the LCM of 78288 and 78304.

LCM(78288,78304) = 2⁵ × 3¹ × 7¹ × 233¹ × 2447¹
LCM(78288,78304) = 383141472