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Suppose 'a' and 'b' are two numbers. The HCF of 'a' and 'b' is 4 and the LCM is 400. So what can be the value of the number of pairs 'a' and 'b'?
1. 3
2. 4
3. 2
4. 1

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Correct Answer - Option 3 : 2

Given:

HCF = 4

LCM = 400 

Concept used:

If the number a = 4x and b = 4y, then HCF = 4

Where x and y will be the co-prime.

Formula used:

LCM × HCF = a × b

Calculation:

HCF is 4. So numbers are multiples of 4

Let the numbers be 4x and 4y.

LCM × HCF = a × b

⇒ 400 × 4 = 4x × 4y

⇒ 1600 =16xy

⇒ xy = 100

Here,  x and y will be the co-prime.

Then, possible pairs are (1, 100), (4, 25)

∴ There will be 2 such possible pairs.

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