What is the Least Common Multiple of 31740 and 31760?

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 31740 and 31760 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31740 and 31760, than apply into the LCM equation.

GCF(31740,31760) = 20
LCM(31740,31760) = ( 31740 × 31760) / 20
LCM(31740,31760) = 1008062400 / 20
LCM(31740,31760) = 50403120

Least Common Multiple (LCM) of 31740 and 31760 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31740 and 31760. First we will calculate the prime factors of 31740 and 31760.

Prime Factorization of 31740

Prime Factorization of 31760

Now multiplying the highest exponent prime factors to calculate the LCM of 31740 and 31760.

LCM(31740,31760) = 2⁴ × 3¹ × 5¹ × 23² × 397¹
LCM(31740,31760) = 50403120