What is the Least Common Multiple of 8505 and 8514?

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 8505 and 8514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8505 and 8514, than apply into the LCM equation.

GCF(8505,8514) = 9
LCM(8505,8514) = ( 8505 × 8514) / 9
LCM(8505,8514) = 72411570 / 9
LCM(8505,8514) = 8045730

Least Common Multiple (LCM) of 8505 and 8514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8505 and 8514. First we will calculate the prime factors of 8505 and 8514.

Prime Factorization of 8505

Prime Factorization of 8514

Now multiplying the highest exponent prime factors to calculate the LCM of 8505 and 8514.

LCM(8505,8514) = 3⁵ × 5¹ × 7¹ × 2¹ × 11¹ × 43¹
LCM(8505,8514) = 8045730