The smallest number divisible by both 6 and 9 is 18.
Understanding Divisibility and the Least Common Multiple (LCM)
When we talk about a number being divisible by another, it means that the division results in a whole number with no remainder. In the context of this question, we are looking for a number that can be divided by both 6 and 9 without leaving any remainder. The smallest such number is known as the Least Common Multiple (LCM).
Finding the LCM
The reference provided clearly states that the LCM of 6 and 9 is 18.
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Checking divisibility:
- 18 / 6 = 3 (no remainder)
- 18 / 9 = 2 (no remainder)
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Why not 36?:
While 36 is also divisible by both 6 and 9, it's not the smallest such number.- 36 / 6 = 6 (no remainder)
- 36 / 9 = 4 (no remainder)
As the reference explains, 18 is the LCM for 6 and 9, not 36.
Why is the LCM Important?
The LCM is important in various mathematical and real-world applications, especially when dealing with fractions, time intervals, and repetitive tasks.
For instance:
- Fractions: When adding or subtracting fractions with different denominators, the LCM of the denominators is used to find a common denominator.
- Scheduling: If one event occurs every 6 hours, and another every 9 hours, the LCM (18 hours) is the first time they will occur together.
Conclusion
Therefore, the smallest number that is divisible by both 6 and 9 is definitively 18. This is due to 18 being the Least Common Multiple (LCM) of 6 and 9, as verified by the provided reference.
