What is the Least Common Multiple of 76400 and 76414?

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 76400 and 76414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 76400 and 76414, than apply into the LCM equation.

GCF(76400,76414) = 2
LCM(76400,76414) = ( 76400 × 76414) / 2
LCM(76400,76414) = 5838029600 / 2
LCM(76400,76414) = 2919014800

Least Common Multiple (LCM) of 76400 and 76414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 76400 and 76414. First we will calculate the prime factors of 76400 and 76414.

Prime Factorization of 76400

Prime Factorization of 76414

Now multiplying the highest exponent prime factors to calculate the LCM of 76400 and 76414.

LCM(76400,76414) = 2⁴ × 5² × 191¹ × 13¹ × 2939¹
LCM(76400,76414) = 2919014800