What is the Least Common Multiple of 31990 and 31997?

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 31990 and 31997 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31990 and 31997, than apply into the LCM equation.

GCF(31990,31997) = 7
LCM(31990,31997) = ( 31990 × 31997) / 7
LCM(31990,31997) = 1023584030 / 7
LCM(31990,31997) = 146226290

Least Common Multiple (LCM) of 31990 and 31997 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31990 and 31997. First we will calculate the prime factors of 31990 and 31997.

Prime Factorization of 31990

Prime Factorization of 31997

Now multiplying the highest exponent prime factors to calculate the LCM of 31990 and 31997.

LCM(31990,31997) = 2¹ × 5¹ × 7² × 457¹ × 653¹
LCM(31990,31997) = 146226290