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:

1. M : N : O = 2 : 3 : 5

2. 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):

• 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

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