What is the Least Common Multiple of 78240 and 78260?

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 78240 and 78260 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78240 and 78260, than apply into the LCM equation.

GCF(78240,78260) = 20
LCM(78240,78260) = ( 78240 × 78260) / 20
LCM(78240,78260) = 6123062400 / 20
LCM(78240,78260) = 306153120

Least Common Multiple (LCM) of 78240 and 78260 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78240 and 78260. First we will calculate the prime factors of 78240 and 78260.

Prime Factorization of 78240

Prime Factorization of 78260

Now multiplying the highest exponent prime factors to calculate the LCM of 78240 and 78260.

LCM(78240,78260) = 2⁵ × 3¹ × 5¹ × 163¹ × 7¹ × 13¹ × 43¹
LCM(78240,78260) = 306153120