What is the Least Common Multiple of 3500 and 3514?

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 3500 and 3514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3500 and 3514, than apply into the LCM equation.

GCF(3500,3514) = 14
LCM(3500,3514) = ( 3500 × 3514) / 14
LCM(3500,3514) = 12299000 / 14
LCM(3500,3514) = 878500

Least Common Multiple (LCM) of 3500 and 3514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 3500 and 3514. First we will calculate the prime factors of 3500 and 3514.

Prime Factorization of 3500

Prime Factorization of 3514

Now multiplying the highest exponent prime factors to calculate the LCM of 3500 and 3514.

LCM(3500,3514) = 2² × 5³ × 7¹ × 251¹
LCM(3500,3514) = 878500