- 21/3
- 71/4
- 51/2
- 31/4
- 31/2

Option 3 : 51/2

**Concept Used:**

Take lcm of powers to get the largest number out of (a^{m}, b^{n})

**Calculations:**

Numbers = 21/3, 31/4, 51/2 and 71/4,

Lcm of (3, 4, 2, 4) = 12

Multiplying powers of all numbers by 12, we get

Numbers = 2^{12 × }1/3, 3^{12 × }1/4, 5^{12 ×}1/2 and 7^{12 ×}1/4

⇒ Numbers = 2^{4}, 3^{3}, 5^{6} and 7^{3}

⇒ Numbers = 16, 27, 15625 and 343

Largest number = 15625

⇒ Out of given numbers, largest number = 5^{1/2}

**∴ The largest number is 51/2.**

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