What is the Least Common Multiple of 31224 and 31234?

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 31224 and 31234 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31224 and 31234, than apply into the LCM equation.

GCF(31224,31234) = 2
LCM(31224,31234) = ( 31224 × 31234) / 2
LCM(31224,31234) = 975250416 / 2
LCM(31224,31234) = 487625208

Least Common Multiple (LCM) of 31224 and 31234 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31224 and 31234. First we will calculate the prime factors of 31224 and 31234.

Prime Factorization of 31224

Prime Factorization of 31234

Now multiplying the highest exponent prime factors to calculate the LCM of 31224 and 31234.

LCM(31224,31234) = 2³ × 3¹ × 1301¹ × 7¹ × 23¹ × 97¹
LCM(31224,31234) = 487625208