A set of marbles can be divided in equal shares among $2$, $3$, $4$, $5$, or $6$ children with no marbles left over. What is the least number of marbles that the set could have?
Let's call the number of marbles x. So we're trying to find the smallest number x that has 2, 3, 4, 5, and 6 as factors. Right. Let's start by finding the prime factorization of each of these numbers. 2 is a prime number so its prime factorization is just 2. 3 is also a prime number so its prime factorization is just 3. 4 is not a prime number. It is 2*2. 5 is a prime number so its prime factorization is just 5. 6 is not a prime number. It is 2*3. So we need 2, 3, and 5 as factors. Right. We also need 2*2, or 4, as a factor. So we need 2, 3, 4, and 5 as factors. That means we need 2*2*3*5 which is 60. So the smallest set of marbles that can be divided in equal shares among 2, 3, 4, 5, and 6 children with no marbles left over has 60 marbles.

