What is the Least Common Multiple of 13678 and 13688?

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 13678 and 13688 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13678 and 13688, than apply into the LCM equation.

GCF(13678,13688) = 2
LCM(13678,13688) = ( 13678 × 13688) / 2
LCM(13678,13688) = 187224464 / 2
LCM(13678,13688) = 93612232

Least Common Multiple (LCM) of 13678 and 13688 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13678 and 13688. First we will calculate the prime factors of 13678 and 13688.

Prime Factorization of 13678

Prime Factorization of 13688

Now multiplying the highest exponent prime factors to calculate the LCM of 13678 and 13688.

LCM(13678,13688) = 2³ × 7¹ × 977¹ × 29¹ × 59¹
LCM(13678,13688) = 93612232