What is the Least Common Multiple of 10380 and 10400?

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 10380 and 10400 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10380 and 10400, than apply into the LCM equation.

GCF(10380,10400) = 20
LCM(10380,10400) = ( 10380 × 10400) / 20
LCM(10380,10400) = 107952000 / 20
LCM(10380,10400) = 5397600

Least Common Multiple (LCM) of 10380 and 10400 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10380 and 10400. First we will calculate the prime factors of 10380 and 10400.

Prime Factorization of 10380

Prime Factorization of 10400

Now multiplying the highest exponent prime factors to calculate the LCM of 10380 and 10400.

LCM(10380,10400) = 2⁵ × 3¹ × 5² × 173¹ × 13¹
LCM(10380,10400) = 5397600