What is the Least Common Multiple of 78115 and 78120?

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 78115 and 78120 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78115 and 78120, than apply into the LCM equation.

GCF(78115,78120) = 5
LCM(78115,78120) = ( 78115 × 78120) / 5
LCM(78115,78120) = 6102343800 / 5
LCM(78115,78120) = 1220468760

Least Common Multiple (LCM) of 78115 and 78120 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78115 and 78120. First we will calculate the prime factors of 78115 and 78120.

Prime Factorization of 78115

Prime Factorization of 78120

Now multiplying the highest exponent prime factors to calculate the LCM of 78115 and 78120.

LCM(78115,78120) = 5¹ × 17¹ × 919¹ × 2³ × 3² × 7¹ × 31¹
LCM(78115,78120) = 1220468760