Unable to derive any clues from the following. Please help!
Our class planned a holiday party for disadvantaged kids.Some of us baked cookies for the party.On the day of the party,we found we could divide the cookies into packets of two, three, four, five, or six and have just one cookie left over in each case.If we divided them into packets of seven, there would be no cookies left over. What is the least number of cookies the class could have baked?__________.
96 fl oz=how many pints
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16 fl oz = 1 pint
Divide 96 by 16.
To solve this problem, we need to find the least number of cookies that satisfy the given conditions. Let's analyze the clues provided in the question:
1. The cookies can be divided into packets of two, three, four, five, or six, and there is one cookie left over in each case.
2. If the cookies are divided into packets of seven, there are no cookies left over.
First, let's consider the condition that the cookies can be divided into packets of two, three, four, five, or six with exactly one cookie left over. This tells us that the least number of cookies must be a multiple of 2, 3, 4, 5, and 6, plus one.
To find the least common multiple (LCM) of 2, 3, 4, 5, and 6, we can factorize each number:
2: 2 * 1
3: 3 * 1
4: 2 * 2
5: 5 * 1
6: 2 * 3
Now, we take the highest power of each prime factor:
2^2 * 3 * 5 = 60
Adding one to the LCM gives us:
60 + 1 = 61
So, the least number of cookies the class could have baked is 61.