What is the Least Common Multiple of 27984 and 28004?

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 27984 and 28004 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27984 and 28004, than apply into the LCM equation.

GCF(27984,28004) = 4
LCM(27984,28004) = ( 27984 × 28004) / 4
LCM(27984,28004) = 783663936 / 4
LCM(27984,28004) = 195915984

Least Common Multiple (LCM) of 27984 and 28004 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27984 and 28004. First we will calculate the prime factors of 27984 and 28004.

Prime Factorization of 27984

Prime Factorization of 28004

Now multiplying the highest exponent prime factors to calculate the LCM of 27984 and 28004.

LCM(27984,28004) = 2⁴ × 3¹ × 11¹ × 53¹ × 7001¹
LCM(27984,28004) = 195915984