find the least common multiple (lcm) of 10 and 8.

Explanation:

Step1: Prime - factorize the numbers

$10 = 2\times5$; $8 = 2\times2\times2$

Step2: Determine the highest - power factors

For factor 2, the highest power is $2^3$ (from 8). For factor 5, the highest power is $5^1$ (from 10).

Step3: Calculate the LCM

$LCM(10,8)=2^3\times5^1=40$

Answer:

40