What is the Least Common Multiple of 78960 and 78978?

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 78960 and 78978 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78960 and 78978, than apply into the LCM equation.

GCF(78960,78978) = 6
LCM(78960,78978) = ( 78960 × 78978) / 6
LCM(78960,78978) = 6236102880 / 6
LCM(78960,78978) = 1039350480

Least Common Multiple (LCM) of 78960 and 78978 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78960 and 78978. First we will calculate the prime factors of 78960 and 78978.

Prime Factorization of 78960

Prime Factorization of 78978

Now multiplying the highest exponent prime factors to calculate the LCM of 78960 and 78978.

LCM(78960,78978) = 2⁴ × 3¹ × 5¹ × 7¹ × 47¹ × 13163¹
LCM(78960,78978) = 1039350480