What is the Least Common Multiple of 33504 and 33514?

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 33504 and 33514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33504 and 33514, than apply into the LCM equation.

GCF(33504,33514) = 2
LCM(33504,33514) = ( 33504 × 33514) / 2
LCM(33504,33514) = 1122853056 / 2
LCM(33504,33514) = 561426528

Least Common Multiple (LCM) of 33504 and 33514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33504 and 33514. First we will calculate the prime factors of 33504 and 33514.

Prime Factorization of 33504

Prime Factorization of 33514

Now multiplying the highest exponent prime factors to calculate the LCM of 33504 and 33514.

LCM(33504,33514) = 2⁵ × 3¹ × 349¹ × 13¹ × 1289¹
LCM(33504,33514) = 561426528