What is the Least Common Multiple of 13944 and 13964?

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 13944 and 13964 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13944 and 13964, than apply into the LCM equation.

GCF(13944,13964) = 4
LCM(13944,13964) = ( 13944 × 13964) / 4
LCM(13944,13964) = 194714016 / 4
LCM(13944,13964) = 48678504

Least Common Multiple (LCM) of 13944 and 13964 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13944 and 13964. First we will calculate the prime factors of 13944 and 13964.

Prime Factorization of 13944

Prime Factorization of 13964

Now multiplying the highest exponent prime factors to calculate the LCM of 13944 and 13964.

LCM(13944,13964) = 2³ × 3¹ × 7¹ × 83¹ × 3491¹
LCM(13944,13964) = 48678504