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?

Gives me the algebraic expression for each statement Sandra made 3 more batches of cookies than Tommy

To solve this problem, we need to find the least number of cookies that satisfies the following conditions:

1. The number of cookies must be divisible by 2, 3, 4, 5, and 6, leaving one cookie remaining in each case.
2. The number of cookies must be divisible by 7, leaving no cookies remaining.

To find the least number of cookies that satisfy these conditions, we can use a method called "finding the least common multiple (LCM) of the numbers 2, 3, 4, 5, 6, and 7."

Here's how we can find the LCM step by step:

1. List the prime factors of each number:
- 2: 2
- 3: 3
- 4: 2 x 2
- 5: 5
- 6: 2 x 3
- 7: 7

2. Write down the highest power of each prime factor that occurs in any of the factorizations:
- 2: 2^2
- 3: 3
- 4: 2^2
- 5: 5
- 6: 2 x 3
- 7: 7

3. Multiply all the highest powers from Step 2 together:
2^2 x 3 x 5 x 7 = 4 x 3 x 5 x 7 = 420

Therefore, the least number of cookies the class could have baked is 420.