What is the Least Common Multiple of 10506 and 10514?

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 10506 and 10514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10506 and 10514, than apply into the LCM equation.

GCF(10506,10514) = 2
LCM(10506,10514) = ( 10506 × 10514) / 2
LCM(10506,10514) = 110460084 / 2
LCM(10506,10514) = 55230042

Least Common Multiple (LCM) of 10506 and 10514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10506 and 10514. First we will calculate the prime factors of 10506 and 10514.

Prime Factorization of 10506

Prime Factorization of 10514

Now multiplying the highest exponent prime factors to calculate the LCM of 10506 and 10514.

LCM(10506,10514) = 2¹ × 3¹ × 17¹ × 103¹ × 7¹ × 751¹
LCM(10506,10514) = 55230042