still don't get it.....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?__________
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Since divided into bags of 2,3,4,5,6, all left one cookie, we have also another way.
Find the LCM (lowest common multiple) of 2,3,4,5,6. Call this L.
Check if L+1 is divisible by 7. If it is, L is your answer. If it is not, try 2L+1, 3L+1, ... until it is divisible by 7. You will not have to try more than 7 times.
If you are not sure how to find the LCM of 2,3,4,5,6, post again.
To find the least number of cookies the class could have baked, we need to determine the smallest number that satisfies the given conditions.
Let's break down the problem step by step:
1. We know that the class can divide the cookies into packets of 2, 3, 4, 5, or 6, and have one cookie left over in each case.
2. This means that the number of cookies must be one greater than a multiple of 2, 3, 4, 5, and 6.
3. To satisfy these conditions, we can find the least common multiple (LCM) of 2, 3, 4, 5, and 6 and then add one.
Now let's find the LCM of 2, 3, 4, 5, and 6:
The LCM of 2 and 3 is 6.
The LCM of 4 and 6 is 12.
The LCM of 5 and 12 is 60.
Therefore, 60 is the LCM of 2, 3, 4, 5, and 6.
To find the least number of cookies, we add one to the LCM:
60 + 1 = 61.
Therefore, the least number of cookies the class could have baked is 61.