What is the Least Common Multiple of 31710 and 31724?

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 31710 and 31724 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31710 and 31724, than apply into the LCM equation.

GCF(31710,31724) = 14
LCM(31710,31724) = ( 31710 × 31724) / 14
LCM(31710,31724) = 1005968040 / 14
LCM(31710,31724) = 71854860

Least Common Multiple (LCM) of 31710 and 31724 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31710 and 31724. First we will calculate the prime factors of 31710 and 31724.

Prime Factorization of 31710

Prime Factorization of 31724

Now multiplying the highest exponent prime factors to calculate the LCM of 31710 and 31724.

LCM(31710,31724) = 2² × 3¹ × 5¹ × 7¹ × 151¹ × 11¹ × 103¹
LCM(31710,31724) = 71854860