What is the Least Common Multiple of 31440 and 31460?

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 31440 and 31460 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31440 and 31460, than apply into the LCM equation.

GCF(31440,31460) = 20
LCM(31440,31460) = ( 31440 × 31460) / 20
LCM(31440,31460) = 989102400 / 20
LCM(31440,31460) = 49455120

Least Common Multiple (LCM) of 31440 and 31460 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31440 and 31460. First we will calculate the prime factors of 31440 and 31460.

Prime Factorization of 31440

Prime Factorization of 31460

Now multiplying the highest exponent prime factors to calculate the LCM of 31440 and 31460.

LCM(31440,31460) = 2⁴ × 3¹ × 5¹ × 131¹ × 11² × 13¹
LCM(31440,31460) = 49455120