What is the Least Common Multiple of 31577 and 31590?

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 31577 and 31590 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31577 and 31590, than apply into the LCM equation.

GCF(31577,31590) = 13
LCM(31577,31590) = ( 31577 × 31590) / 13
LCM(31577,31590) = 997517430 / 13
LCM(31577,31590) = 76732110

Least Common Multiple (LCM) of 31577 and 31590 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31577 and 31590. First we will calculate the prime factors of 31577 and 31590.

Prime Factorization of 31577

Prime Factorization of 31590

Now multiplying the highest exponent prime factors to calculate the LCM of 31577 and 31590.

LCM(31577,31590) = 7¹ × 13¹ × 347¹ × 2¹ × 3⁵ × 5¹
LCM(31577,31590) = 76732110