What is the Least Common Multiple of 31906 and 31914?

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 31906 and 31914 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31906 and 31914, than apply into the LCM equation.

GCF(31906,31914) = 2
LCM(31906,31914) = ( 31906 × 31914) / 2
LCM(31906,31914) = 1018248084 / 2
LCM(31906,31914) = 509124042

Least Common Multiple (LCM) of 31906 and 31914 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31906 and 31914. First we will calculate the prime factors of 31906 and 31914.

Prime Factorization of 31906

Prime Factorization of 31914

Now multiplying the highest exponent prime factors to calculate the LCM of 31906 and 31914.

LCM(31906,31914) = 2¹ × 7¹ × 43¹ × 53¹ × 3⁴ × 197¹
LCM(31906,31914) = 509124042