What is the Least Common Multiple of 7504 and 7514?

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 7504 and 7514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7504 and 7514, than apply into the LCM equation.

GCF(7504,7514) = 2
LCM(7504,7514) = ( 7504 × 7514) / 2
LCM(7504,7514) = 56385056 / 2
LCM(7504,7514) = 28192528

Least Common Multiple (LCM) of 7504 and 7514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7504 and 7514. First we will calculate the prime factors of 7504 and 7514.

Prime Factorization of 7504

Prime Factorization of 7514

Now multiplying the highest exponent prime factors to calculate the LCM of 7504 and 7514.

LCM(7504,7514) = 2⁴ × 7¹ × 67¹ × 13¹ × 17²
LCM(7504,7514) = 28192528