What is the Least Common Multiple of 414 and 422?

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 414 and 422 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 414 and 422, than apply into the LCM equation.

GCF(414,422) = 2
LCM(414,422) = ( 414 × 422) / 2
LCM(414,422) = 174708 / 2
LCM(414,422) = 87354

Least Common Multiple (LCM) of 414 and 422 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 414 and 422. First we will calculate the prime factors of 414 and 422.

Prime Factorization of 414

Prime Factorization of 422

Now multiplying the highest exponent prime factors to calculate the LCM of 414 and 422.

LCM(414,422) = 2¹ × 3² × 23¹ × 211¹
LCM(414,422) = 87354