What is the Least Common Multiple of 10270 and 10288?

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 10270 and 10288 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10270 and 10288, than apply into the LCM equation.

GCF(10270,10288) = 2
LCM(10270,10288) = ( 10270 × 10288) / 2
LCM(10270,10288) = 105657760 / 2
LCM(10270,10288) = 52828880

Least Common Multiple (LCM) of 10270 and 10288 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10270 and 10288. First we will calculate the prime factors of 10270 and 10288.

Prime Factorization of 10270

Prime Factorization of 10288

Now multiplying the highest exponent prime factors to calculate the LCM of 10270 and 10288.

LCM(10270,10288) = 2⁴ × 5¹ × 13¹ × 79¹ × 643¹
LCM(10270,10288) = 52828880