What is the Least Common Multiple of 13746 and 13760?

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 13746 and 13760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13746 and 13760, than apply into the LCM equation.

GCF(13746,13760) = 2
LCM(13746,13760) = ( 13746 × 13760) / 2
LCM(13746,13760) = 189144960 / 2
LCM(13746,13760) = 94572480

Least Common Multiple (LCM) of 13746 and 13760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13746 and 13760. First we will calculate the prime factors of 13746 and 13760.

Prime Factorization of 13746

Prime Factorization of 13760

Now multiplying the highest exponent prime factors to calculate the LCM of 13746 and 13760.

LCM(13746,13760) = 2⁶ × 3¹ × 29¹ × 79¹ × 5¹ × 43¹
LCM(13746,13760) = 94572480