Question

A set of marbles can be divided into 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?

Answer 1

The smallest number of marbles that can be evenly divided among 2, 3, 4, 5, or 6 children is 60, which is the Least Common Multiple (LCM) of these numbers.

Step-by-step explanation:

The question asks to find the smallest number of marbles that can be evenly divided among 2, 3, 4, 5, or 6 children with no remaining marbles. This means we need to calculate the Least Common Multiple (LCM) of these numbers. The LCM of 2, 3, 4, 5, and 6 is the smallest number that all these numbers can divide into evenly without leaving a remainder.

Calculating the LCM:

1. The prime factors of these numbers are: 2, 3, 2^2 (which is 4), 5, and 2 * 3 (which is 6).
2. To find the LCM, we take the highest power of each prime factor that appears in the factorization of any of these numbers. That results in: 2^2 * 3 * 5.
3. Multiplying these together gives us the LCM: 2^2 = 4, multiplied by 3 = 12, multiplied by 5 equals 60.

Therefore, the smallest number of marbles that can be divided among 2, 3, 4, 5, and 6 children without any remainder is 60 marbles.