If the ratios M:N:O = 2:3:5 and M:N:O = 4:5:6 are given, which of the following is a common multiple of both ratios?

Understand the meaning We are given two ratios and asked to find a common multiple — that is, a set of values for M, N, and O that fits both ratios proportionally. Given Ratios: M : N : O = 2 : 3 : 5 M : N : O = 4 : 5 : 6 We want to find a new ratio X : Y : Z that is proportional to both these given ratios. Check Option B: 8:15:30 Try simplifying 8:15:30: Divide all terms by 1 (GCD is 1, so already simplified): Still 8:15:30 Now check if it fits the first ratio (2:3:5): 8 ÷ 2 = 4 15 ÷ 3 = 5 30 ÷ 5 = 6 So 8:15:30 = 2×4: 3×5: 5×6 = 2:3:5 scaled up by different amounts? No — wait! Those aren’t consistent scalings. Instead, let’s try another way: Divide 8:15:30 by 4: 8 ÷ 4 = 2 15 ÷ 5 = 3 30 ÷ 6 = 5 So 8:15:30 → 2:3:5 (matches first ratio) Now divide 8:15:30 by 2: 8 ÷ 2 = 4 15 ÷ 3 = 5 30 ÷ 5 = 6 So 8:15:30 → 4:5:6 (matches second ratio) 8:15:30 is a common multiple of both 2:3:5 and 4:5:6