What is the Least Common Multiple of 33760 and 33764?

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 33760 and 33764 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33760 and 33764, than apply into the LCM equation.

GCF(33760,33764) = 4
LCM(33760,33764) = ( 33760 × 33764) / 4
LCM(33760,33764) = 1139872640 / 4
LCM(33760,33764) = 284968160

Least Common Multiple (LCM) of 33760 and 33764 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33760 and 33764. First we will calculate the prime factors of 33760 and 33764.

Prime Factorization of 33760

Prime Factorization of 33764

Now multiplying the highest exponent prime factors to calculate the LCM of 33760 and 33764.

LCM(33760,33764) = 2⁵ × 5¹ × 211¹ × 23¹ × 367¹
LCM(33760,33764) = 284968160