What is the Least Common Multiple of 78309 and 78320?

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 78309 and 78320 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78309 and 78320, than apply into the LCM equation.

GCF(78309,78320) = 11
LCM(78309,78320) = ( 78309 × 78320) / 11
LCM(78309,78320) = 6133160880 / 11
LCM(78309,78320) = 557560080

Least Common Multiple (LCM) of 78309 and 78320 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78309 and 78320. First we will calculate the prime factors of 78309 and 78320.

Prime Factorization of 78309

Prime Factorization of 78320

Now multiplying the highest exponent prime factors to calculate the LCM of 78309 and 78320.

LCM(78309,78320) = 3² × 7¹ × 11¹ × 113¹ × 2⁴ × 5¹ × 89¹
LCM(78309,78320) = 557560080