Question

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

Explanation:

Step1: Prime Factorization

Factorize 10 and 8:
$10 = 2 \times 5$
$8 = 2^3$

Step2: Identify Highest Powers

For each prime factor, take the highest power:

• Prime 2: highest power is $2^3$ (from 8)
• Prime 5: highest power is $5^1$ (from 10)

Step3: Calculate LCM

Multiply these highest powers:
$\text{LCM} = 2^3 \times 5 = 8 \times 5 = 40$

Answer:

40