What is the LCM of 3, 6, and 9?

The multiples of 3, 6, and 9 are:

• Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, …
• Multiples of 6: 6, 12, 18, 24, 30, 36, 42, …
• Multiples of 9: 9, 18, 27, 36, 45, …

To find the LCM of 3, 6, and 9, we need to find the smallest number that is a multiple of all three. We can start by listing the multiples of the largest number, 9, and checking which one is also a multiple of the other two numbers, 3 and 6:

• 9 is a multiple of 3 and 9 is a multiple of 6, so 9 is a common multiple.
• 18 is a multiple of 3 and 6, but it is not a multiple of 9.
• 27 is a multiple of 3 and 9, but it is not a multiple of 6.
• 36 is a multiple of 6 and 9, and it is also the smallest multiple that is common to all three numbers.

Therefore, the LCM of 3, 6, and 9 is 36.