Multiple choice

The HCF of two numbers of same number of digits is 45 and their LCM is 540. The numbers are

  1. 270, 540

  2. 135, 270

  3. 180, 270

  4. 135, 180
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D Correct answer
Explanation

For two numbers with HCF 45 and LCM 540, their product is 45 * 540 = 24300. The numbers must be multiples of 45, such as 45a and 45b where a and b are coprime. 45a * 45b = 24300 implies ab = 12. Possible pairs for (a,b) are (1,12) and (3,4). The numbers are (45, 540) or (135, 180). Since both must have the same number of digits, 135 and 180 are the correct pair.

AI explanation

Let the numbers be 45a and 45b, where a and b are coprime. The LCM is 45ab = 540, so ab = 12. Checking the pairs of factors of 12, the pair (3, 4) yields the numbers 135 and 180. The numbers are 135 and 180.

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