What is the Least Common Multiple of 78400 and 78414?

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 78400 and 78414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 78400 and 78414, than apply into the LCM equation.

GCF(78400,78414) = 14
LCM(78400,78414) = ( 78400 × 78414) / 14
LCM(78400,78414) = 6147657600 / 14
LCM(78400,78414) = 439118400

Least Common Multiple (LCM) of 78400 and 78414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 78400 and 78414. First we will calculate the prime factors of 78400 and 78414.

Prime Factorization of 78400

Prime Factorization of 78414

Now multiplying the highest exponent prime factors to calculate the LCM of 78400 and 78414.

LCM(78400,78414) = 2⁶ × 5² × 7² × 3¹ × 1867¹
LCM(78400,78414) = 439118400