This question confuses me...
Identify a number thatis divisible by 17, 3, and 9, which is not divisible by 7, 18, 5, 16, and 14.Describe how you found this answer.
please help me!!
17 * 3 * 9 = 459
Is 459 divisible by 7, 18, 5, 16, and 14?
thx. can u help me with a few more problems?
To identify a number that is divisible by 17, 3, and 9, but not divisible by 7, 18, 5, 16, and 14, we need to find the Least Common Multiple (LCM) of 17, 3, and 9. The LCM is the smallest number that is evenly divisible by all the given numbers.
First, let's find the LCM of 17 and 3. To do this, we can list the multiples of each number until we find a common multiple.
Multiples of 17: 17, 34, 51, 68, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, ...
From the lists, we can see that the first common multiple of 17 and 3 is 51.
Now, let's find the LCM of 51 and 9. Similarly, we list the multiples of each number until we find a common multiple.
Multiples of 51: 51, 102, 153, 204, ...
Multiples of 9: 9, 18, 27, 36, 45, 54, ...
The first common multiple of 51 and 9 is 153.
So, the LCM of 17, 3, and 9 is 153.
Now, we need to check if this number is not divisible by 7, 18, 5, 16, and 14.
Divisibility by 7: Since 153 is not divisible by 7 (as there is no remainder when you divide 153 by 7), it satisfies this condition.
Divisibility by 18: 153 divided by 18 equals 8 with a remainder of 9. Since there is a remainder, 153 is not divisible by 18.
Divisibility by 5: 153 divided by 5 equals 30 with a remainder of 3. Since there is a remainder, 153 is not divisible by 5.
Divisibility by 16: 153 divided by 16 equals 9 with a remainder of 9. Since there is a remainder, 153 is not divisible by 16.
Divisibility by 14: 153 divided by 14 equals 10 with a remainder of 13. Since there is a remainder, 153 is not divisible by 14.
Therefore, a number that is divisible by 17, 3, and 9, but not divisible by 7, 18, 5, 16, and 14 is 153.