What is the Least Common Multiple of 13974 and 13978?

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 13974 and 13978 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13974 and 13978, than apply into the LCM equation.

GCF(13974,13978) = 2
LCM(13974,13978) = ( 13974 × 13978) / 2
LCM(13974,13978) = 195328572 / 2
LCM(13974,13978) = 97664286

Least Common Multiple (LCM) of 13974 and 13978 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13974 and 13978. First we will calculate the prime factors of 13974 and 13978.

Prime Factorization of 13974

Prime Factorization of 13978

Now multiplying the highest exponent prime factors to calculate the LCM of 13974 and 13978.

LCM(13974,13978) = 2¹ × 3¹ × 17¹ × 137¹ × 29¹ × 241¹
LCM(13974,13978) = 97664286