What is the least possible number of marbles in a box containing red and blue marbles in a ratio 7:4

well try 11

of course you could do 14/ 8 which gives 22
or
28/16 etc etc but they asked for the LEAST

The least number of marbles in a box is 11

Very good 😊

To find the least possible number of marbles in a box containing red and blue marbles in a ratio of 7:4, we need to determine the common multiple of both 7 and 4.

First, let's assign some variables:
Let's say the ratio is 7x:4x, where x is a positive integer.

Now, we'll find the least common multiple (LCM) of 7 and 4. The LCM of two numbers is the smallest number that both numbers can divide into evenly.

The prime factorization of 7 is 7, and the prime factorization of 4 is 2^2.

To find the LCM, we take the highest power of each prime factor that appears in either number. In this case, 7^1 * 2^2 = 28.

So, the least possible number of marbles in the box would be 28 marbles. The box would contain 7 * 4 = 28 red and 4 * 4 = 16 blue marbles, in a ratio of 7:4.