Question : Two numbers are in the ratio 9 : 7. If their HCF is 6, find their LCM.
Option 1: 189
Option 2: 126
Option 3: 378
Option 4: 252
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Correct Answer: 378
Solution : Let the two numbers be A and B. According to the question, $A = 9x$ and $B = 7x$ HCF of A and B is $x$. Given: HCF of these two numbers = 8 ⇒ $x = 8$ $A = 9x = 9 × 6 = 54$ $B = 7x = 7 × 6 = 42$ $\therefore$ LCM of 54 and 42 = 378 Hence, the correct answer is 378.
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Question : The ratio of the LCM of two numbers to the sum of the same two numbers is 12 : 7. If their HCF is 4, what is the product of these two numbers?
Option 1: 192
Option 2: 172
Option 3: 196
Option 4: 169
Question : If the heights of two cylinders are in the ratio of 7 : 9 and their diameters are in the ratio of 6 : 7, then what is the ratio of the volumes of the cylinders?
Option 1: 6 : 7
Option 2: 7 : 9
Option 3: 5 : 9
Option 4: 4 : 7
Question : Three numbers are in the ratio 2 : 3 : 5 and their LCM is 60. What is the HCF of the numbers?
Option 1: 2
Option 2: 4
Option 3: 10
Option 4: 6
Question : Two numbers are in the ratio 11 : 6. If their HCF is 4, find the smallest number.
Option 1: 30
Option 2: 18
Option 3: 24
Option 4: 12
Question : The LCM of the two numbers is 4 times their HCF. The sum of LCM and HCF is 125. If one of the numbers is 100, then the other number is:
Option 1: 5
Option 2: 25
Option 3: 100
Option 4: 125
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