What is the Least Common Multiple of 67200 and 67209?

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 67200 and 67209 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67200 and 67209, than apply into the LCM equation.

GCF(67200,67209) = 3
LCM(67200,67209) = ( 67200 × 67209) / 3
LCM(67200,67209) = 4516444800 / 3
LCM(67200,67209) = 1505481600

Least Common Multiple (LCM) of 67200 and 67209 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67200 and 67209. First we will calculate the prime factors of 67200 and 67209.

Prime Factorization of 67200

Prime Factorization of 67209

Now multiplying the highest exponent prime factors to calculate the LCM of 67200 and 67209.

LCM(67200,67209) = 2⁷ × 3¹ × 5² × 7¹ × 43¹ × 521¹
LCM(67200,67209) = 1505481600