The HCF and LCM of two number are 21 and 4641, respectively.

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The HCF and LCM of two number are 21 and 4641, respectively. If one of the numbers lies between 200 and 300, then find the two numbers.

1. 273, 363
2. 273, 359
3. 273, 361
4. 273, 357
5. None of the above

Correct Option: D

Let the numbers be 21a and 21b, where a and b are co-primes.
Then, 21a x 21b = (21 x 4641)
⇒ ab = 221
Two co-primes with product 221 are 13 and 17.
∴ Required number = (21 x 13, 21 x 17)
= (273, 357)