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15 x 14 x13 x... x 3 x 2 x 1 = 3^m x n

Where m and n are positive integers, then what is the maximum value of m?

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Complete-Test, Previous year (2022)

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Explanation:

15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3^m × n
Numbers which are multiple of 3 = 15 × 12 × 9 × 6 × 3 = (3 × 5) × (3 × 4) × (3 × 3) × (3 × 2) × 3 = 36 × (5 ×4 × 2)
Therefore, the maximum value of m is 6.
Hence, option (b) is the correct answer.

By: Munesh Kumari

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