What is the Least Common Multiple of 67188 and 67200?

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 67188 and 67200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67188 and 67200, than apply into the LCM equation.

GCF(67188,67200) = 12
LCM(67188,67200) = ( 67188 × 67200) / 12
LCM(67188,67200) = 4515033600 / 12
LCM(67188,67200) = 376252800

Least Common Multiple (LCM) of 67188 and 67200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67188 and 67200. First we will calculate the prime factors of 67188 and 67200.

Prime Factorization of 67188

Prime Factorization of 67200

Now multiplying the highest exponent prime factors to calculate the LCM of 67188 and 67200.

LCM(67188,67200) = 2⁷ × 3¹ × 11¹ × 509¹ × 5² × 7¹
LCM(67188,67200) = 376252800