What is the Least Common Multiple of 13748 and 13762?

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 13748 and 13762 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13748 and 13762, than apply into the LCM equation.

GCF(13748,13762) = 14
LCM(13748,13762) = ( 13748 × 13762) / 14
LCM(13748,13762) = 189199976 / 14
LCM(13748,13762) = 13514284

Least Common Multiple (LCM) of 13748 and 13762 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13748 and 13762. First we will calculate the prime factors of 13748 and 13762.

Prime Factorization of 13748

Prime Factorization of 13762

Now multiplying the highest exponent prime factors to calculate the LCM of 13748 and 13762.

LCM(13748,13762) = 2² × 7¹ × 491¹ × 983¹
LCM(13748,13762) = 13514284