Mr Barkley has a box of books. He says the number of books in the box is divisible by 2,3,4,5 and 6. How many books could be in the box? Add another condition to the number of so that there is only one possible solution.
Multiples of 6:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78
Which of those numbers is also divisible by 2, 3, 4, and 5?
To find the number of books that could be in Mr. Barkley's box, we need to find the least common multiple (LCM) of 2, 3, 4, 5, and 6. The LCM is the smallest positive integer divisible by all of these numbers. Here's how you can calculate the LCM:
1. Prime factorize each number:
- Prime factorization of 2: 2
- Prime factorization of 3: 3
- Prime factorization of 4: 2^2
- Prime factorization of 5: 5
- Prime factorization of 6: 2 * 3
2. Take the highest power of each prime factor that appears in any of the prime factorizations of the given numbers:
- Highest power of 2: 2^2 = 4
- Highest power of 3: 3
- Highest power of 5: 5
3. Multiply the highest powers of the prime factors together:
LCM = 4 * 3 * 5 = 60
So, the number of books in Mr. Barkley's box could be 60.
To add another condition that gives only one possible solution, we can specify that the number of books in the box must be the LCM itself, which is 60 in this case.