What is the Least Common Multiple of 4200 and 4219?

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 4200 and 4219 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 4200 and 4219, than apply into the LCM equation.

GCF(4200,4219) = 1
LCM(4200,4219) = ( 4200 × 4219) / 1
LCM(4200,4219) = 17719800 / 1
LCM(4200,4219) = 17719800

Least Common Multiple (LCM) of 4200 and 4219 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 4200 and 4219. First we will calculate the prime factors of 4200 and 4219.

Prime Factorization of 4200

Prime Factorization of 4219

Now multiplying the highest exponent prime factors to calculate the LCM of 4200 and 4219.

LCM(4200,4219) = 2³ × 3¹ × 5² × 7¹ × 4219¹
LCM(4200,4219) = 17719800