What is the Least Common Multiple of 67209 and 67216?

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 67209 and 67216 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67209 and 67216, than apply into the LCM equation.

GCF(67209,67216) = 1
LCM(67209,67216) = ( 67209 × 67216) / 1
LCM(67209,67216) = 4517520144 / 1
LCM(67209,67216) = 4517520144

Least Common Multiple (LCM) of 67209 and 67216 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67209 and 67216. First we will calculate the prime factors of 67209 and 67216.

Prime Factorization of 67209

Prime Factorization of 67216

Now multiplying the highest exponent prime factors to calculate the LCM of 67209 and 67216.

LCM(67209,67216) = 3¹ × 43¹ × 521¹ × 2⁴ × 4201¹
LCM(67209,67216) = 4517520144