The HCF and LCM of two numbers are 26 and 910 respectively. If one of the numbers lies between 150 and 250, then that number is
Explanation:
Since HCF is 26, let us assume that the numbers are 26x and 26y
∴ Product of the two numbers = HCF × LCM = 26x × 26y
⇒ 26x × 26y = 26 × 910
∴ xy = 35
Now, we have to write 35 as a product two co-prime numbers, hence
35 = 1 × 35 (one of x and y is 1 and the other is 35) 35 = 7 × 5 (one of x and y is 7 and the other is 5)
The numbers can be 26 × 1, 26 × 35 or 26 × 5, 26 × 7
Only one number lies within the given limits, 26 × 7 = 182.
Hence, option (a).
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