What is the Least Common Multiple of 27980 and 28000?

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 27980 and 28000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 27980 and 28000, than apply into the LCM equation.

GCF(27980,28000) = 20
LCM(27980,28000) = ( 27980 × 28000) / 20
LCM(27980,28000) = 783440000 / 20
LCM(27980,28000) = 39172000

Least Common Multiple (LCM) of 27980 and 28000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 27980 and 28000. First we will calculate the prime factors of 27980 and 28000.

Prime Factorization of 27980

Prime Factorization of 28000

Now multiplying the highest exponent prime factors to calculate the LCM of 27980 and 28000.

LCM(27980,28000) = 2⁵ × 5³ × 1399¹ × 7¹
LCM(27980,28000) = 39172000