What is the Least Common Multiple of 31674 and 31680?

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 31674 and 31680 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31674 and 31680, than apply into the LCM equation.

GCF(31674,31680) = 6
LCM(31674,31680) = ( 31674 × 31680) / 6
LCM(31674,31680) = 1003432320 / 6
LCM(31674,31680) = 167238720

Least Common Multiple (LCM) of 31674 and 31680 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31674 and 31680. First we will calculate the prime factors of 31674 and 31680.

Prime Factorization of 31674

Prime Factorization of 31680

Now multiplying the highest exponent prime factors to calculate the LCM of 31674 and 31680.

LCM(31674,31680) = 2⁶ × 3² × 5279¹ × 5¹ × 11¹
LCM(31674,31680) = 167238720