Question : The HCF and LCM of two numbers are 9 and 126, respectively. Find the larger number, if the ratio between the numbers is 2 : 7.
Option 1: 42
Option 2: 63
Option 3: 77
Option 4: 21
Correct Answer: 63
Solution : Let's denote the two numbers as $2x$ and $7x$ (where $x$ is a positive integer) The product of the two numbers is equal to the product of their HCF and LCM: ⇒ $(2x)(7x)$ = HCF $\times$ LCM Given, HCF = 9 and the LCM = 126 ⇒ $(2x)(7x)=9\times126$ ⇒ $14x^2=1134$ ⇒ $x^2=81$ ⇒ $x=9$ $\therefore$ Larger number = 7 × 9 = 63 Hence, the correct answer is 63.
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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
Question : The HCF and LCM of the two numbers are 126 and 9 respectively. If one of the numbers is 18, then what is the other number?
Option 1: 63
Option 2: 36
Option 3: 84
Option 4: 24
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 : Directions: Which two numbers should be interchanged to make the given equation correct? 63 ÷ 21 – 42 + 8 × 7 = 135
Option 1: 7 and 63
Option 2: 7 and 21
Option 3: 21 and 42
Option 4: 21 and 8
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
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