Explanation:
the lowest common denominator (LCD) is the lowest common multiple (LCM) of the denominator numbers (the ones at the bottom of the fractions).
finding the LCM of 9 and 12 using the prime factor method :
9 = 3×3
12 = 2×2×3
the LCM is the combination of the longest chains per prime factor. which means we have 2×2 and 3×3 as longest chains for 2 and 3.
LCD = LCM = 2×2×3×3 = 36
2/9 turns into x/36 by multiplying by 4/4 :
2/9 × 4/4 = 8/36
5/12 turns into x/36 by multiplying by 3/3 :
5/12 × 3/3 = 15/36
so, the third answer option is correct.