What is the Least Common Multiple of 72210 and 72214?

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 72210 and 72214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72210 and 72214, than apply into the LCM equation.

GCF(72210,72214) = 2
LCM(72210,72214) = ( 72210 × 72214) / 2
LCM(72210,72214) = 5214572940 / 2
LCM(72210,72214) = 2607286470

Least Common Multiple (LCM) of 72210 and 72214 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 72210 and 72214. First we will calculate the prime factors of 72210 and 72214.

Prime Factorization of 72210

Prime Factorization of 72214

Now multiplying the highest exponent prime factors to calculate the LCM of 72210 and 72214.

LCM(72210,72214) = 2¹ × 3¹ × 5¹ × 29¹ × 83¹ × 36107¹
LCM(72210,72214) = 2607286470