What is the Least Common Multiple of 10056 and 10074?

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 10056 and 10074 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10056 and 10074, than apply into the LCM equation.

GCF(10056,10074) = 6
LCM(10056,10074) = ( 10056 × 10074) / 6
LCM(10056,10074) = 101304144 / 6
LCM(10056,10074) = 16884024

Least Common Multiple (LCM) of 10056 and 10074 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10056 and 10074. First we will calculate the prime factors of 10056 and 10074.

Prime Factorization of 10056

Prime Factorization of 10074

Now multiplying the highest exponent prime factors to calculate the LCM of 10056 and 10074.

LCM(10056,10074) = 2³ × 3¹ × 419¹ × 23¹ × 73¹
LCM(10056,10074) = 16884024