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The HCF and LCM of two positive numbers are 26 and 910 respectively. If one of the numbers is 130, then what is the other number?

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180

182

105

answer is B.

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Detailed Solution

It is given that the HCF and LCM of two positive numbers are 26 and 910 respectively.

Let the two positive numbers be a and b, where a = 130

It is known that for any positive integers a and b,

HCF (a, b) × LCM (a, b) = a × b

∴ HCF (130, b) × LCM (130, b) = 130 × b

⇒ 26 × 910 = 130 × b

$b = \frac{26 \times 910}{130}$

$= 182$

Thus, the other number is 182.

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