What is the Least Common Multiple of 10074 and 10083?

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 10074 and 10083 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10074 and 10083, than apply into the LCM equation.

GCF(10074,10083) = 3
LCM(10074,10083) = ( 10074 × 10083) / 3
LCM(10074,10083) = 101576142 / 3
LCM(10074,10083) = 33858714

Least Common Multiple (LCM) of 10074 and 10083 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10074 and 10083. First we will calculate the prime factors of 10074 and 10083.

Prime Factorization of 10074

Prime Factorization of 10083

Now multiplying the highest exponent prime factors to calculate the LCM of 10074 and 10083.

LCM(10074,10083) = 2¹ × 3¹ × 23¹ × 73¹ × 3361¹
LCM(10074,10083) = 33858714