Namid works for a florist and is making arrangements for the tables at a reception . He has 36 roses, 48 tulips, and 72 carnations. Each vase must contain the same number of each type of flower. How many vases will Namid need. How many of each type of flower will he put in one vase?

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To find out how many vases Namid will need and how many of each type of flower will go in one vase, we need to find the greatest common divisor (GCD) of the three numbers: 36, 48, and 72.

Step 1: Find the prime factors of each number:
- The prime factors of 36 are 2² * 3² (2 * 2 * 3 * 3).
- The prime factors of 48 are 2⁴ * 3¹ (2 * 2 * 2 * 2 * 3).
- The prime factors of 72 are 2³ * 3² (2 * 2 * 2 * 3 * 3).

Step 2: Identify the common prime factors and their lowest exponents:
- We have two 2's and two 3's that are common to all three numbers (2² * 3²).

Step 3: Multiply the common prime factors with their lowest exponents:
- The GCD of 36, 48, and 72 is 2² * 3², which is equal to 4 * 9 = 36.

Therefore, Namid will need 36 vases, and each vase will contain 2 roses, 3 tulips, and 4 carnations.

36 = 2^2 * 3^2

38 = 2^4 * 3
72 = 2^3 * 3^2
the greatest common factor of those three is 2^2 * 3 = 12
so, make 12 vases, each with
36/12 = 3 roses
48/12 = 4 tulips
72/12 = 6 carnations