What is the Least Common Multiple of 78105 and 78114?

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 78105 and 78114 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78105 and 78114, than apply into the LCM equation.

GCF(78105,78114) = 3
LCM(78105,78114) = ( 78105 × 78114) / 3
LCM(78105,78114) = 6101093970 / 3
LCM(78105,78114) = 2033697990

Least Common Multiple (LCM) of 78105 and 78114 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78105 and 78114. First we will calculate the prime factors of 78105 and 78114.

Prime Factorization of 78105

Prime Factorization of 78114

Now multiplying the highest exponent prime factors to calculate the LCM of 78105 and 78114.

LCM(78105,78114) = 3¹ × 5¹ × 41¹ × 127¹ × 2¹ × 47¹ × 277¹
LCM(78105,78114) = 2033697990