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# There are 75 rose and 45 lily flowers. These are to be made into bouquets containing both the flowers. All the bouquets should contain the same number of flowers. Find the number of bouquets with maximum number of flowers that can be formed and the number of flowers in them.

Last updated date: 20th Jun 2024
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Hint: We will first consider the given data and then we will find the factors of the given values 75 and 45. After this we need to find the maximum number of flowers contained in one bouquet by finding the highest common factor obtained from the factors of 75 and 45. Next to find the number of flowers in the bouquet can be found by adding the factors of highest common factors.

Complete step by step solution:
First consider the number of roses that is 75 and number of lilies that is 45.
Now, we will find the factors of number 75
We get,
Factors of $75 = 3 \times 5 \times 5$
Next, we will find the factors of the number 45,
Thus, we have,
$\Rightarrow 45 = 3 \times 3 \times 5$
Now, to determine the maximum number of flowers contained in one bouquet, we are required to find the highest common factor (H.C.F) from these two factors.
Thus, the common factors from both the numbers are 3 and 5
Thus, we get the H.C.F. as,
$\Rightarrow 3 \times 5 = 15$
Hence, the numbers of flowers contained in one bouquet are $15$.
And the numbers of flowers in the bouquets can be found by adding 3 and 5
Thus, we get,
$\Rightarrow 3 + 5 = 8$.
Which means the number of rose flowers in the bouquets is 5 and the number of lily flowers in the bouquets is 3.

Note: Do not think to find out the LCM, if we find the LCM then we get the minimum number of flowers, so that answer can be wrong. To find the maximum number of flowers, the highest common factor has to be calculated. To find the total numbers just add the common factors obtained from the factorization.