There are some flowers in a basket.if these are distributed among 12 children equally,8flowers remain and if these flowers are distributed among 14children equally,10flowers remain. What is the minimum number flowers in the baskets

To find the minimum number of flowers in the basket, we need to consider the two scenarios given:

1. If the flowers are distributed among 12 children equally and 8 flowers remain:
Let's assume the total number of flowers in the basket is "x". If these are distributed among 12 children, each child will receive x/12 flowers. Since 8 flowers remain, the equation representing this scenario would be: x mod 12 = 8 (mod represents the remainder operator).

2. If the flowers are distributed among 14 children equally and 10 flowers remain:
Similarly, let's assume the total number of flowers in the basket is "y". If these are distributed among 14 children, each child will receive y/14 flowers. Since 10 flowers remain, the equation representing this scenario would be: y mod 14 = 10.

To find the minimum number of flowers that satisfy both scenarios, we need to find a common solution for both equations.

Solving the first equation:
x mod 12 = 8
We can iteratively substitute values for x and check if the equation holds true. Starting with x = 8, we get 8 mod 12 = 8, which is true. Hence, 8 is a possible solution.

Solving the second equation:
y mod 14 = 10
Again, we can iteratively substitute values for y and check if the equation holds true. Starting with y = 10, we get 10 mod 14 = 10, which is true. Hence, 10 is a possible solution.

To find the minimum number of flowers in the basket, we need to find the least common multiple (LCM) of 12 and 14 since it represents the number of flowers that satisfies both scenarios. LCM(12, 14) = 84.

Therefore, the minimum number of flowers in the basket is 84.