What is the Least Common Multiple of 86400 and 86419?

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 86400 and 86419 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 86400 and 86419, than apply into the LCM equation.

GCF(86400,86419) = 1
LCM(86400,86419) = ( 86400 × 86419) / 1
LCM(86400,86419) = 7466601600 / 1
LCM(86400,86419) = 7466601600

Least Common Multiple (LCM) of 86400 and 86419 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 86400 and 86419. First we will calculate the prime factors of 86400 and 86419.

Prime Factorization of 86400

Prime Factorization of 86419

Now multiplying the highest exponent prime factors to calculate the LCM of 86400 and 86419.

LCM(86400,86419) = 2⁷ × 3³ × 5² × 89¹ × 971¹
LCM(86400,86419) = 7466601600