The smallest number divisible by 6, 9, and 15 is 90.
This number is also known as the Least Common Multiple (LCM) of 6, 9, and 15. Here's how we can determine that:
Understanding Least Common Multiple (LCM)
The LCM of a set of numbers is the smallest positive integer that is a multiple of all the numbers in that set. In our case, we need a number that is divisible by 6, 9, and 15.
Methods to find the LCM:
One method is to list out the multiples of each number until we find a common one.
| Number | Multiples |
|---|---|
| 6 | 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90,... |
| 9 | 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ... |
| 15 | 15, 30, 45, 60, 75, 90,... |
As shown above, 90 is the first number that appears in all the lists of multiples.
According to the provided reference, the LCM of 6, 9, and 15 is 90. The reference further explains, "choose the smallest multiple that is exactly divisible by 6, 9, and 15, i.e., 90."
Why LCM is Important?
- LCM helps in solving problems related to time and measurements.
- It is also useful in mathematical and real-world situations, such as combining fractions with different denominators.
Therefore, 90 is indeed the smallest number that is divisible by 6, 9, and 15.
