What is the least common denominator (LCD) of the numbers 3, 4, 4, 5, 2, and 3?

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The least common denominator (LCD) is the smallest number that can be divided evenly by each of the denominators in a set of fractions. To find the LCD for the numbers 3, 4, 4, 5, 2, and 3, we need to follow a systematic approach:

  1. Identify the numbers: We have the numbers 3, 4, 4, 5, 2, and 3.
  2. List the prime factors:
    • 3: 3
    • 4: 2 x 2
    • 5: 5
    • 2: 2
  3. Collect the highest powers of each prime number:
    • For the prime number 2, the highest power is 22 (from 4).
    • For the prime number 3, the highest power is 31 (from 3).
    • For the prime number 5, the highest power is 51 (from 5).
  4. Calculate the least common denominator: Multiply the highest powers of all prime factors:
    LCD = 22 x 31 x 51
    LCD = 4 x 3 x 5
    LCD = 60

So, the least common denominator (LCD) of 3, 4, 4, 5, 2, and 3 is 60.

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