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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