To find the smallest number that gives a remainder of 5 when divided by 16, 24, and 18, we can use the concept of the least common multiple (LCM) of these numbers.
The LCM of 16, 24, and 18 is 144.
To find the smallest number that gives a remainder of 5 when divided by these three numbers, we can add 5 to the LCM:
144 + 5 = 149
Therefore, the smallest number that satisfies the given conditions is 149.
Sure, I'd be happy to help explain this problem in a way that is easy to understand!
To find the smallest number which when divided by 16, 24, and 18 gives a remainder of 5, we can use a method called "trial and error".
First, we can start by adding 5 to multiples of 16 until we find a number that gives a remainder of 5 when divided by both 24 and 18. For example:
- 5 + 16 = 21 (not divisible by 24 or 18)
- 5 + 32 = 37 (not divisible by 24 or 18)
- 5 + 48 = 53 (not divisible by 24 or 18)
- 5 + 64 = 69 (divisible by 24 and gives a remainder of 5 when divided by 18)
So we know that the number we're looking for is at least 69. We can continue this process by adding multiples of 16 x 24 (which is the same as adding multiples of 384) to see if we can find a smaller number that satisfies all three conditions.
- 69 + 384 = 453 (not divisible by 18)
- 69 + 2 x 384 = 837 (divisible by 18 and gives a remainder of 5 when divided by 24)
Therefore, the smallest number that satisfies all three conditions is 837.
To check our answer, we can divide 837 by each of the three divisors and make sure that we get a remainder of 5 in each case:
- 837 ÷ 16 = 52 with a remainder of 5
- 837 ÷ 24 = 34 with a remainder of 5
- 837 ÷ 18 = 46 with a remainder of 5
So we can be confident that our answer is correct.
Answers & Comments
Answer:
To find the smallest number that gives a remainder of 5 when divided by 16, 24, and 18, we can use the concept of the least common multiple (LCM) of these numbers.
The LCM of 16, 24, and 18 is 144.
To find the smallest number that gives a remainder of 5 when divided by these three numbers, we can add 5 to the LCM:
144 + 5 = 149
Therefore, the smallest number that satisfies the given conditions is 149.
Answer:
Sure, I'd be happy to help explain this problem in a way that is easy to understand!
To find the smallest number which when divided by 16, 24, and 18 gives a remainder of 5, we can use a method called "trial and error".
First, we can start by adding 5 to multiples of 16 until we find a number that gives a remainder of 5 when divided by both 24 and 18. For example:
- 5 + 16 = 21 (not divisible by 24 or 18)
- 5 + 32 = 37 (not divisible by 24 or 18)
- 5 + 48 = 53 (not divisible by 24 or 18)
- 5 + 64 = 69 (divisible by 24 and gives a remainder of 5 when divided by 18)
So we know that the number we're looking for is at least 69. We can continue this process by adding multiples of 16 x 24 (which is the same as adding multiples of 384) to see if we can find a smaller number that satisfies all three conditions.
- 69 + 384 = 453 (not divisible by 18)
- 69 + 2 x 384 = 837 (divisible by 18 and gives a remainder of 5 when divided by 24)
Therefore, the smallest number that satisfies all three conditions is 837.
To check our answer, we can divide 837 by each of the three divisors and make sure that we get a remainder of 5 in each case:
- 837 ÷ 16 = 52 with a remainder of 5
- 837 ÷ 24 = 34 with a remainder of 5
- 837 ÷ 18 = 46 with a remainder of 5
So we can be confident that our answer is correct.
Hope that helps!