What is the Least Common Multiple of 19904 and 19914?

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 19904 and 19914 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19904 and 19914, than apply into the LCM equation.

GCF(19904,19914) = 2
LCM(19904,19914) = ( 19904 × 19914) / 2
LCM(19904,19914) = 396368256 / 2
LCM(19904,19914) = 198184128

Least Common Multiple (LCM) of 19904 and 19914 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 19904 and 19914. First we will calculate the prime factors of 19904 and 19914.

Prime Factorization of 19904

Prime Factorization of 19914

Now multiplying the highest exponent prime factors to calculate the LCM of 19904 and 19914.

LCM(19904,19914) = 2⁶ × 311¹ × 3¹ × 3319¹
LCM(19904,19914) = 198184128