What is the least common denominator of 3, 4, 4, 5, 2, 3?

To find the least common denominator (LCD) of the numbers 3, 4, 4, 5, 2, and 3, we first identify the prime factors of each number:

• 3:     3
• 4:     2 × 2
• 5:     5
• 2:     2

Next, we take the highest power of each prime number that appears in the factorization of the numbers. The primes we have are 2, 3, and 5:

• Highest power of 2:     2² (from 4)
• Highest power of 3:     3¹ (from 3)
• Highest power of 5:     5¹ (from 5)

Now, we multiply these highest powers together to get the least common denominator:

LCD = 2² × 3¹ × 5¹ = 4 × 3 × 5 = 60

Therefore, the least common denominator of 3, 4, 4, 5, 2, and 3 is 60.