The least common denominator (LCD) for 2/3 and 1/6 is 6. To find equivalent fractions that correctly use the LCD, we need to find the equivalent fractions of 2/3 and 1/6 with a denominator of 6.
2/3 is equivalent to 4/6 (multiply the numerator and denominator by 2)
1/6 is equivalent to 1/6 (multiply the numerator and denominator by 1)
Therefore, the set of equivalent fractions that correctly uses the LCD for 2/3 and 1/6 is 4/6 and 1/6.
So, the answer is 4/6 and 1/6.