A group of friends went to a coffee shop.
2/5 bought coffee
1/3 bought tea
4/15 bought cake
What is the smallest posible number of people in the group?
15
(6/15 + 5/15 + 4/15)x = x
looks like 15 to me. There is no smaller common denominator
To find the smallest possible number of people in the group, we need to find the least common multiple (LCM) of the denominators of the fractions. In this case, the denominators are 5, 3, and 15.
To find the LCM, we can list the multiples of each number and look for the smallest common multiple:
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, ...
Multiples of 15: 15, 30, 45, 60, ...
The smallest common multiple is 15. Therefore, the smallest possible number of people in the group is 15.
Note: In this case, the denominators happened to have a common multiple, but that might not always be the case. In general, to find the LCM, you can use prime factorization method or the division method.