What is the Least Common Multiple of 78128 and 78138?

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 78128 and 78138 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78128 and 78138, than apply into the LCM equation.

GCF(78128,78138) = 2
LCM(78128,78138) = ( 78128 × 78138) / 2
LCM(78128,78138) = 6104765664 / 2
LCM(78128,78138) = 3052382832

Least Common Multiple (LCM) of 78128 and 78138 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78128 and 78138. First we will calculate the prime factors of 78128 and 78138.

Prime Factorization of 78128

Prime Factorization of 78138

Now multiplying the highest exponent prime factors to calculate the LCM of 78128 and 78138.

LCM(78128,78138) = 2⁴ × 19¹ × 257¹ × 3³ × 1447¹
LCM(78128,78138) = 3052382832