What is the Least Common Multiple of 32400 and 32419?

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 32400 and 32419 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32400 and 32419, than apply into the LCM equation.

GCF(32400,32419) = 1
LCM(32400,32419) = ( 32400 × 32419) / 1
LCM(32400,32419) = 1050375600 / 1
LCM(32400,32419) = 1050375600

Least Common Multiple (LCM) of 32400 and 32419 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32400 and 32419. First we will calculate the prime factors of 32400 and 32419.

Prime Factorization of 32400

Prime Factorization of 32419

Now multiplying the highest exponent prime factors to calculate the LCM of 32400 and 32419.

LCM(32400,32419) = 2⁴ × 3⁴ × 5² × 17¹ × 1907¹
LCM(32400,32419) = 1050375600