A book is between 400 and 450 pages. If we count them 2 at a time there is none left over, if we count them 5 at a time there is none left over and if we count them 7 at a time there are none left over, how many pages does the book have?

To find the number of pages in the book, we need to find the least common multiple (LCM) of the numbers 2, 5, and 7. The LCM is the smallest multiple that is divisible by all three numbers. LCM(2, 5, 7) = LCM(LCM(2, 5), 7) = LCM(10, 7) Now, let's find the LCM of 10 and 7. We can use the following formula to find the LCM: LCM(a, b) = (a * b) / GCD(a, b) Here, GCD represents the greatest common divisor. GCD(10, 7) = 1 (since 10 and 7 are relatively prime) Now, we can find the LCM: LCM(10, 7) = (10 * 7) / 1 = 70 So, the book has 70 pages.