Question

Find the smallest number that is divisible by each of 8, 9, and 10.

Answer 1

Step 1: Understand the problem:
We are tasked with finding the smallest number that is divisible by 8, 9, and 10. This number is known as the Least Common Multiple (LCM) of 8, 9, and 10.

Step 2: Find the prime factorization of each number:
To find the LCM, we first find the prime factorization of each number:
- $8 = 2^3$
- $9 = 3^2$
- $10 = 2 \times 5$

Step 3: Determine the LCM:
The LCM is found by taking the highest power of each prime factor that appears in the factorizations. We have the following prime factors:
- The highest power of 2 is $2^3$ (from 8)
- The highest power of 3 is $3^2$ (from 9)
- The highest power of 5 is $5^1$ (from 10)
Therefore, the LCM is: \[ \text{LCM} = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 360 \]

Step 4: Conclusion:
The smallest number that is divisible by 8, 9, and 10 is 360.