Bryan is making balloon arrangements. He has 8 blue balloons and 12 green balloons. What is the greatest amount of arrangements he can make if he wants them identical?
HCF of 8 and 12 is 4
so he can make 4 same arrangements, each consisting of 2 reds and 3 greens
To find the greatest amount of arrangements that Bryan can make with identical blue and green balloons, we need to determine the maximum number of arrangements possible using the smaller quantity of balloons (in this case, the blue balloons).
Since Bryan has 8 blue balloons, he can make a maximum of 8 arrangements using only blue balloons.
Therefore, the greatest amount of arrangements he can make with identical blue and green balloons is 8.
To find the greatest amount of identical arrangements, we need to determine the least common multiple (LCM) of the two numbers of balloons.
To find the LCM of 8 and 12, we can follow these steps:
1. List the prime factors of each number: The prime factorization of 8 is 2 x 2 x 2 and the prime factorization of 12 is 2 x 2 x 3.
2. Write down all the prime factors that appear in either number: 2 x 2 x 2 x 3.
3. Multiply all the prime factors: 2 x 2 x 2 x 3 = 24.
Therefore, the LCM of 8 and 12 is 24. This means that the greatest amount of identical arrangements Bryan can make is 24.