What is the Least Common Multiple of 1506 and 1514?

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 1514 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 1514, than apply into the LCM equation.

GCF(1506,1514) = 2
LCM(1506,1514) = ( 1506 × 1514) / 2
LCM(1506,1514) = 2280084 / 2
LCM(1506,1514) = 1140042

Least Common Multiple (LCM) of 1506 and 1514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1506 and 1514. First we will calculate the prime factors of 1506 and 1514.

Prime Factorization of 1506

Prime Factorization of 1514

Now multiplying the highest exponent prime factors to calculate the LCM of 1506 and 1514.

LCM(1506,1514) = 2¹ × 3¹ × 251¹ × 757¹
LCM(1506,1514) = 1140042