What is the Least Common Multiple of 33744 and 33760?

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 33744 and 33760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 33744 and 33760, than apply into the LCM equation.

GCF(33744,33760) = 16
LCM(33744,33760) = ( 33744 × 33760) / 16
LCM(33744,33760) = 1139197440 / 16
LCM(33744,33760) = 71199840

Least Common Multiple (LCM) of 33744 and 33760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33744 and 33760. First we will calculate the prime factors of 33744 and 33760.

Prime Factorization of 33744

Prime Factorization of 33760

Now multiplying the highest exponent prime factors to calculate the LCM of 33744 and 33760.

LCM(33744,33760) = 2⁵ × 3¹ × 19¹ × 37¹ × 5¹ × 211¹
LCM(33744,33760) = 71199840