What is the Least Common Multiple of 34214 and 34224?

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 34214 and 34224 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34214 and 34224, than apply into the LCM equation.

GCF(34214,34224) = 2
LCM(34214,34224) = ( 34214 × 34224) / 2
LCM(34214,34224) = 1170939936 / 2
LCM(34214,34224) = 585469968

Least Common Multiple (LCM) of 34214 and 34224 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 34214 and 34224. First we will calculate the prime factors of 34214 and 34224.

Prime Factorization of 34214

Prime Factorization of 34224

Now multiplying the highest exponent prime factors to calculate the LCM of 34214 and 34224.

LCM(34214,34224) = 2⁴ × 17107¹ × 3¹ × 23¹ × 31¹
LCM(34214,34224) = 585469968