Question : The sum of and difference between the LCM and HCF of two numbers are 512 and 496, respectively. If one number is 72, then the other number is:
Option 1: 56
Option 2: 64
Option 3: 40
Option 4: 80
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Correct Answer: 56
Solution : Let the two numbers as 'a' and 'b', where a = 72 (given). According to the problem, ⇒ LCM + HCF = 512 ⇒ LCM – HCF = 496 We can solve these two equations to find the values of LCM and HCF. Adding the two equations, ⇒ 2LCM = 512 + 496 = 1008 ⇒ LCM = 504 Substituting LCM = 504 in the first equation, ⇒ 504 + HCF = 512 ⇒ HCF = 512 – 504 = 8 Now, we know that the product of two numbers is equal to the product of their LCM and HCF. ⇒ a × b = LCM × HCF ⇒ 72 × b = 504 × 8 ⇒ b = 56 So, the other number is 56 Hence, the correct answer is 56.
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