Divisibility Problem: Finding Numbers Divisible by 2, 4, and 5 Between 19-29

A nursery distributes an equal number of flowers every day so that no flowers are left undistributed in the field.

On the first day they were divided into pairs.

On the second day they were divided into 4 equal groups.

On the third day they were divided into 5 groups.

It is known that the number of flowers is greater than 19 and less than 29.

Calculate the number of flowers that are distributed in the nursery over the three days.

To solve the problem, we first determine the LCM of the numbers 2, 4, and 5:

• The prime factors of 2 are $2$.
• The prime factors of 4 are $2^2$.
• The prime factors of 5 are $5$.

The LCM is determined by taking the highest power of each prime number: $2^2$ and $5$, so $\text{LCM}(2, 4, 5) = 2^2 \times 5 = 20$.

Next, we consider numbers between 19 and 29: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29.
Among these, only 20 is divisible by 20.

Therefore, the number of flowers is $20$.

So, the solution to the problem is: $\text{Number of flowers} = 20$.