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?
Explanation
Step 1: 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:
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M : N : O = 2 : 3 : 5
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M : N : O = 4 : 5 : 6
We want to find a new ratio X : Y : Z that is proportional to both these given ratios.
Step 2: 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):
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8 ÷ 2 = 4
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15 ÷ 3 = 5
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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:
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8 ÷ 4 = 2
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15 ÷ 5 = 3
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30 ÷ 6 = 5
So 8:15:30 → 2:3:5 (matches first ratio)
Now divide 8:15:30 by 2:
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8 ÷ 2 = 4
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15 ÷ 3 = 5
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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
