What is the smallest number divisible by 1 9?

The question is ambiguous. It could mean:

1. What is the smallest number divisible by both 1 and 9?
2. What is the smallest number divisible by all integers from 1 to 9 (inclusive)?

We will answer both interpretations.

Interpretation 1: Smallest Number Divisible by 1 and 9

The smallest number divisible by both 1 and 9 is 9. Any number divisible by 9 is also divisible by 1.

Interpretation 2: Smallest Number Divisible by 1 Through 9

The smallest number divisible by all the integers from 1 to 9 is their Least Common Multiple (LCM). To find the LCM, we can use prime factorization.

• 1 = 1
• 2 = 2
• 3 = 3
• 4 = 2 x 2 = 2²
• 5 = 5
• 6 = 2 x 3
• 7 = 7
• 8 = 2 x 2 x 2 = 2³
• 9 = 3 x 3 = 3²

To find the LCM, take the highest power of each prime number that appears in the factorizations:

• 2³ = 8
• 3² = 9
• 5 = 5
• 7 = 7

Multiply these together: 8 x 9 x 5 x 7 = 2520.

Therefore, the smallest number divisible by all integers from 1 to 9 is 2520.