What is the Least Common Multiple of 33760 and 33768?

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 33768 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 33768, than apply into the LCM equation.

GCF(33760,33768) = 8
LCM(33760,33768) = ( 33760 × 33768) / 8
LCM(33760,33768) = 1140007680 / 8
LCM(33760,33768) = 142500960

Least Common Multiple (LCM) of 33760 and 33768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 33760 and 33768. First we will calculate the prime factors of 33760 and 33768.

Prime Factorization of 33760

Prime Factorization of 33768

Now multiplying the highest exponent prime factors to calculate the LCM of 33760 and 33768.

LCM(33760,33768) = 2⁵ × 5¹ × 211¹ × 3² × 7¹ × 67¹
LCM(33760,33768) = 142500960