What is the Least Common Multiple of 67104 and 67116?

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 67104 and 67116 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67104 and 67116, than apply into the LCM equation.

GCF(67104,67116) = 12
LCM(67104,67116) = ( 67104 × 67116) / 12
LCM(67104,67116) = 4503752064 / 12
LCM(67104,67116) = 375312672

Least Common Multiple (LCM) of 67104 and 67116 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67104 and 67116. First we will calculate the prime factors of 67104 and 67116.

Prime Factorization of 67104

Prime Factorization of 67116

Now multiplying the highest exponent prime factors to calculate the LCM of 67104 and 67116.

LCM(67104,67116) = 2⁵ × 3² × 233¹ × 7¹ × 17¹ × 47¹
LCM(67104,67116) = 375312672