What is the Least Common Multiple of 31760 and 31768?

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 31760 and 31768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31760 and 31768, than apply into the LCM equation.

GCF(31760,31768) = 8
LCM(31760,31768) = ( 31760 × 31768) / 8
LCM(31760,31768) = 1008951680 / 8
LCM(31760,31768) = 126118960

Least Common Multiple (LCM) of 31760 and 31768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31760 and 31768. First we will calculate the prime factors of 31760 and 31768.

Prime Factorization of 31760

Prime Factorization of 31768

Now multiplying the highest exponent prime factors to calculate the LCM of 31760 and 31768.

LCM(31760,31768) = 2⁴ × 5¹ × 397¹ × 11¹ × 19²
LCM(31760,31768) = 126118960