Baking Cookies-Word Problem
Our class planned a 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 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?
To solve this problem, we need to find the least number of cookies that satisfies the given conditions. Let's break down the problem step by step:
1. Cookies leave a remainder of 1 when divided into packets of 2, 3, 4, 5, or 6, but no remainder when divided into packets of 7. This means the number of cookies must be one more than a multiple of 2, 3, 4, 5, and 6, respectively.
2. Now, let's find the least common multiple (LCM) of 2, 3, 4, 5, and 6. The LCM is the smallest number that is divisible by all the given numbers. In this case, the LCM is 60.
3. Since the number of cookies must be one more than the LCM, the least number of cookies the class could have baked is 60 + 1 = 61.
Therefore, the least number of cookies the class could have baked is 61.