What is the Least Common Multiple of 12408 and 12419?

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 12408 and 12419 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12408 and 12419, than apply into the LCM equation.

GCF(12408,12419) = 11
LCM(12408,12419) = ( 12408 × 12419) / 11
LCM(12408,12419) = 154094952 / 11
LCM(12408,12419) = 14008632

Least Common Multiple (LCM) of 12408 and 12419 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12408 and 12419. First we will calculate the prime factors of 12408 and 12419.

Prime Factorization of 12408

Prime Factorization of 12419

Now multiplying the highest exponent prime factors to calculate the LCM of 12408 and 12419.

LCM(12408,12419) = 2³ × 3¹ × 11¹ × 47¹ × 1129¹
LCM(12408,12419) = 14008632