What is the Least Common Multiple of 82004 and 82012?

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 82004 and 82012 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 82004 and 82012, than apply into the LCM equation.

GCF(82004,82012) = 4
LCM(82004,82012) = ( 82004 × 82012) / 4
LCM(82004,82012) = 6725312048 / 4
LCM(82004,82012) = 1681328012

Least Common Multiple (LCM) of 82004 and 82012 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 82004 and 82012. First we will calculate the prime factors of 82004 and 82012.

Prime Factorization of 82004

Prime Factorization of 82012

Now multiplying the highest exponent prime factors to calculate the LCM of 82004 and 82012.

LCM(82004,82012) = 2² × 13¹ × 19¹ × 83¹ × 7¹ × 29¹ × 101¹
LCM(82004,82012) = 1681328012