What is the Least Common Multiple of 13978 and 13988?

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 13978 and 13988 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13978 and 13988, than apply into the LCM equation.

GCF(13978,13988) = 2
LCM(13978,13988) = ( 13978 × 13988) / 2
LCM(13978,13988) = 195524264 / 2
LCM(13978,13988) = 97762132

Least Common Multiple (LCM) of 13978 and 13988 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13978 and 13988. First we will calculate the prime factors of 13978 and 13988.

Prime Factorization of 13978

Prime Factorization of 13988

Now multiplying the highest exponent prime factors to calculate the LCM of 13978 and 13988.

LCM(13978,13988) = 2² × 29¹ × 241¹ × 13¹ × 269¹
LCM(13978,13988) = 97762132