Milan must choose a number between
55
and
101
that is a multiple of
6
,
9
, and
18
Multiples of 18:
72, 90
To find a number between 55 and 101 that is a multiple of 6, 9, and 18, we need to find the smallest common multiple of these three numbers.
The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, ...
The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ...
The multiples of 18 are: 18, 36, 54, 72, 90, 108, ...
By looking at the lists, we can see that the smallest common multiple of 6, 9, and 18 is 54. However, this number is not between 55 and 101.
The next common multiple is 72, which falls between 55 and 101. Therefore, Milan should choose the number 72 as it is a multiple of 6, 9, and 18 and falls between 55 and 101.
To find a number between 55 and 101 that is a multiple of 6, 9, and 18, you need to find the least common multiple (LCM) of those three numbers.
Step 1: Find the LCM of 6 and 9.
The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, and so on.
The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, and so on.
From the lists above, we can see that the LCM of 6 and 9 is 18.
Step 2: Find the LCM of 18 and 18.
The multiples of 18 are: 18, 36, 54, 72, 90, and so on.
From the list above, we can see that the LCM of 18 and 18 is 18.
Therefore, the LCM of 6, 9, and 18 is 18.
Now, we need to find a number between 55 and 101 that is a multiple of 18.
The multiples of 18 between 55 and 101 are: 72 and 90.
Therefore, Milan can choose either 72 or 90 as a number between 55 and 101 that is a multiple of 6, 9, and 18.