What is the Least Common Multiple of 72208 and 72219?

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 72208 and 72219 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72208 and 72219, than apply into the LCM equation.

GCF(72208,72219) = 1
LCM(72208,72219) = ( 72208 × 72219) / 1
LCM(72208,72219) = 5214789552 / 1
LCM(72208,72219) = 5214789552

Least Common Multiple (LCM) of 72208 and 72219 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72208 and 72219. First we will calculate the prime factors of 72208 and 72219.

Prime Factorization of 72208

Prime Factorization of 72219

Now multiplying the highest exponent prime factors to calculate the LCM of 72208 and 72219.

LCM(72208,72219) = 2⁴ × 4513¹ × 3¹ × 7¹ × 19¹ × 181¹
LCM(72208,72219) = 5214789552