What is the Least Common Multiple of 13760 and 13765?

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 13760 and 13765 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13760 and 13765, than apply into the LCM equation.

GCF(13760,13765) = 5
LCM(13760,13765) = ( 13760 × 13765) / 5
LCM(13760,13765) = 189406400 / 5
LCM(13760,13765) = 37881280

Least Common Multiple (LCM) of 13760 and 13765 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13760 and 13765. First we will calculate the prime factors of 13760 and 13765.

Prime Factorization of 13760

Prime Factorization of 13765

Now multiplying the highest exponent prime factors to calculate the LCM of 13760 and 13765.

LCM(13760,13765) = 2⁶ × 5¹ × 43¹ × 2753¹
LCM(13760,13765) = 37881280