What is the Least Common Multiple of 65985 and 66000?

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 65985 and 66000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 65985 and 66000, than apply into the LCM equation.

GCF(65985,66000) = 15
LCM(65985,66000) = ( 65985 × 66000) / 15
LCM(65985,66000) = 4355010000 / 15
LCM(65985,66000) = 290334000

Least Common Multiple (LCM) of 65985 and 66000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 65985 and 66000. First we will calculate the prime factors of 65985 and 66000.

Prime Factorization of 65985

Prime Factorization of 66000

Now multiplying the highest exponent prime factors to calculate the LCM of 65985 and 66000.

LCM(65985,66000) = 3¹ × 5³ × 53¹ × 83¹ × 2⁴ × 11¹
LCM(65985,66000) = 290334000