Question

An old woman goes to market and a horse steps on her basket and crashes the eggs. the rider offers to pay for the damages and asks her how many eggs she had brought. 3 she does not remember the exact number, but when she had taken them out five at a time, there were two eggs left. the same happened when she picked them out nine at a time, but when she took them seven at a time they came out three. what is the smallest number of eggs she could have had?

Answer 1

Answer

Find the LCM by Step 1: Finding the prime factors of each number:


2 is a prime, 3 is a prime, 4 factors to 2*2, 5 is prime, 6 factors to 2*3


Step 2: Look at each prime number represented. Whichever factor group has the most of that number, use that many of that prime number in a product that will be the LCM:


The most 2's are in the factorization of 4, so use 2*2. There are at most one 3 (in the prime factorization of 3 or 6). There are at most one 5.


The LCM is 2*2*3*5 = 60. LCM + 1 is 61. But 61 isn't divisible by 7.



Now increase by 60 (add 1 to multiples of 60) until you find one divisible by 7.

The right answer is 301