What is the Least Common Multiple of 26400 and 26414?

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 26400 and 26414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 26400 and 26414, than apply into the LCM equation.

GCF(26400,26414) = 2
LCM(26400,26414) = ( 26400 × 26414) / 2
LCM(26400,26414) = 697329600 / 2
LCM(26400,26414) = 348664800

Least Common Multiple (LCM) of 26400 and 26414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 26400 and 26414. First we will calculate the prime factors of 26400 and 26414.

Prime Factorization of 26400

Prime Factorization of 26414

Now multiplying the highest exponent prime factors to calculate the LCM of 26400 and 26414.

LCM(26400,26414) = 2⁵ × 3¹ × 5² × 11¹ × 47¹ × 281¹
LCM(26400,26414) = 348664800