What is the Least Common Multiple of 1506 and 1523?

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 1506 and 1523 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1506 and 1523, than apply into the LCM equation.

GCF(1506,1523) = 1
LCM(1506,1523) = ( 1506 × 1523) / 1
LCM(1506,1523) = 2293638 / 1
LCM(1506,1523) = 2293638

Least Common Multiple (LCM) of 1506 and 1523 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1506 and 1523. First we will calculate the prime factors of 1506 and 1523.

Prime Factorization of 1506

Prime Factorization of 1523

Now multiplying the highest exponent prime factors to calculate the LCM of 1506 and 1523.

LCM(1506,1523) = 2¹ × 3¹ × 251¹ × 1523¹
LCM(1506,1523) = 2293638