What is the Least Common Multiple of 19968 and 19978?

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 19968 and 19978 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19968 and 19978, than apply into the LCM equation.

GCF(19968,19978) = 2
LCM(19968,19978) = ( 19968 × 19978) / 2
LCM(19968,19978) = 398920704 / 2
LCM(19968,19978) = 199460352

Least Common Multiple (LCM) of 19968 and 19978 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19968 and 19978. First we will calculate the prime factors of 19968 and 19978.

Prime Factorization of 19968

Prime Factorization of 19978

Now multiplying the highest exponent prime factors to calculate the LCM of 19968 and 19978.

LCM(19968,19978) = 2⁹ × 3¹ × 13¹ × 7¹ × 1427¹
LCM(19968,19978) = 199460352