What is the Least Common Multiple of 408 and 419?

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 408 and 419 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 408 and 419, than apply into the LCM equation.

GCF(408,419) = 1
LCM(408,419) = ( 408 × 419) / 1
LCM(408,419) = 170952 / 1
LCM(408,419) = 170952

Least Common Multiple (LCM) of 408 and 419 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 408 and 419. First we will calculate the prime factors of 408 and 419.

Prime Factorization of 408

Prime Factorization of 419

Now multiplying the highest exponent prime factors to calculate the LCM of 408 and 419.

LCM(408,419) = 2³ × 3¹ × 17¹ × 419¹
LCM(408,419) = 170952