What is the Least Common Multiple of 31504 and 31514?

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 31504 and 31514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31504 and 31514, than apply into the LCM equation.

GCF(31504,31514) = 2
LCM(31504,31514) = ( 31504 × 31514) / 2
LCM(31504,31514) = 992817056 / 2
LCM(31504,31514) = 496408528

Least Common Multiple (LCM) of 31504 and 31514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31504 and 31514. First we will calculate the prime factors of 31504 and 31514.

Prime Factorization of 31504

Prime Factorization of 31514

Now multiplying the highest exponent prime factors to calculate the LCM of 31504 and 31514.

LCM(31504,31514) = 2⁴ × 11¹ × 179¹ × 7¹ × 2251¹
LCM(31504,31514) = 496408528