what is my number
I am a three digit number
I am less than 200
i am divisible by 12 and by 9
my units digit is less than my tens digit
So the range of numbers is 100-199.
Divisible by 12 it is an even number.
Divisible by 9 the digits of the number add up to a number divisible by 9.
So numbers that are divisible by 9 are:
108
117
126
135
144
153
162
171
180
189
198
That are also even and divisible by 12 are:
108
144
180
so which one complies with the last criteria?
But check my working!
180
what is the answer
153
180
To find the three-digit number that satisfies the given conditions, we can break down the problem step by step.
Step 1: Divide 200 by 12 to find the largest possible value of the tens digit.
200 ÷ 12 = 16 remainder 8
So, the largest possible value for the tens digit is 16.
Step 2: Since the units digit must be less than the tens digit, we can start by thinking about the possible values for the units digit. It can be any number from 0 to 7 (since 8 is not less than 16).
Step 3: Next, we need to find a number that is both divisible by 12 and by 9. To do this, we can find the least common multiple (LCM) of 12 and 9, and look for a number that is less than 200.
The LCM of 12 and 9 is 36.
Step 4: List out the numbers that are less than 200 and divisible by 36. We can start with 36 and keep adding 36 until we reach the maximum value (less than 200) for the units digit.
36, 72, 108, 144, 180
Step 5: From this list, we can see that the units digit must be 4, as 4 is the largest value less than the tens digit (16).
Therefore, the three-digit number that is less than 200, divisible by both 12 and 9, and has a units digit less than the tens digit is 144.