What is the Least Common Multiple of 40500 and 40514?

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 40500 and 40514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 40500 and 40514, than apply into the LCM equation.

GCF(40500,40514) = 2
LCM(40500,40514) = ( 40500 × 40514) / 2
LCM(40500,40514) = 1640817000 / 2
LCM(40500,40514) = 820408500

Least Common Multiple (LCM) of 40500 and 40514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 40500 and 40514. First we will calculate the prime factors of 40500 and 40514.

Prime Factorization of 40500

Prime Factorization of 40514

Now multiplying the highest exponent prime factors to calculate the LCM of 40500 and 40514.

LCM(40500,40514) = 2² × 3⁴ × 5³ × 47¹ × 431¹
LCM(40500,40514) = 820408500