What is the Least Common Multiple of 31720 and 31738?

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 31720 and 31738 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31720 and 31738, than apply into the LCM equation.

GCF(31720,31738) = 2
LCM(31720,31738) = ( 31720 × 31738) / 2
LCM(31720,31738) = 1006729360 / 2
LCM(31720,31738) = 503364680

Least Common Multiple (LCM) of 31720 and 31738 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31720 and 31738. First we will calculate the prime factors of 31720 and 31738.

Prime Factorization of 31720

Prime Factorization of 31738

Now multiplying the highest exponent prime factors to calculate the LCM of 31720 and 31738.

LCM(31720,31738) = 2³ × 5¹ × 13¹ × 61¹ × 7¹ × 2267¹
LCM(31720,31738) = 503364680