What is the Least Common Multiple of 67200 and 67219?

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 67219 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 67219, than apply into the LCM equation.

GCF(67200,67219) = 1
LCM(67200,67219) = ( 67200 × 67219) / 1
LCM(67200,67219) = 4517116800 / 1
LCM(67200,67219) = 4517116800

Least Common Multiple (LCM) of 67200 and 67219 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67200 and 67219. First we will calculate the prime factors of 67200 and 67219.

Prime Factorization of 67200

Prime Factorization of 67219

Now multiplying the highest exponent prime factors to calculate the LCM of 67200 and 67219.

LCM(67200,67219) = 2⁷ × 3¹ × 5² × 7¹ × 67219¹
LCM(67200,67219) = 4517116800