What is the Least Common Multiple of 12357 and 12374?

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 12357 and 12374 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12357 and 12374, than apply into the LCM equation.

GCF(12357,12374) = 1
LCM(12357,12374) = ( 12357 × 12374) / 1
LCM(12357,12374) = 152905518 / 1
LCM(12357,12374) = 152905518

Least Common Multiple (LCM) of 12357 and 12374 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12357 and 12374. First we will calculate the prime factors of 12357 and 12374.

Prime Factorization of 12357

Prime Factorization of 12374

Now multiplying the highest exponent prime factors to calculate the LCM of 12357 and 12374.

LCM(12357,12374) = 3² × 1373¹ × 2¹ × 23¹ × 269¹
LCM(12357,12374) = 152905518