Question : The HCF and the LCM of two numbers are 5 and 175, respectively. If the ratio of the two numbers is 5 : 7, the larger of the two numbers is _______.
Option 1: 35
Option 2: 25
Option 3: 45
Option 4: 75
Correct Answer: 35
Solution : Given: HCF of the two numbers = 5 LCM = 175 Let the two numbers be $5x$ and $7x$ We know that, The product of the two numbers = HCF × LCM ⇒ $5x \times 7x = 5 \times 175$ ⇒ $x^2 = \frac{175}{7}$ ⇒ $x^2 = 25$ ⇒ $x = 5$ The larger number is $7x=7\times5=35$ Hence, the correct answer is 35.
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Question : The ratio of the two numbers is 5 : 7 and their HCF is 3. Their LCM is:
Option 1: 75
Option 2: 105
Option 3: 125
Option 4: 35
Question : Two numbers are in the ratio 12 : 7. If their HCF is 25, find the numbers.
Option 1: 225 and 135
Option 2: 300 and 175
Option 3: 300 and 50
Option 4: 175 and 120
Question : The LCM of two numbers is five times their HCF. If the product of the two numbers is 20480, then find their HCF and LCM, respectively.
Option 1: 46 and 230
Option 2: 48 and 240
Option 3: 64 and 320
Option 4: 56 and 280
Question : The LCM and HCF of the two numbers are 1105 and 5. If the LCM is 17 times the first number, then find the two numbers.
Option 1: 65 and 85
Option 2: 55 and 85
Option 3: 65 and 75
Option 4: 60 and 80
Question : Two numbers are in the ratio 3 : 4. The product of their HCF and LCM is 2700. The sum of the numbers is:
Option 1: 60
Option 3: 15
Option 4: 45
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