Question : The LCM of four consecutive numbers is 60. The sum of the first two numbers is equal to the fourth number. What is the sum of the four numbers?
Option 1: 17
Option 2: 14
Option 3: 21
Option 4: 24
Correct Answer: 14
Solution : Let the 1st number be 'x'. 2nd number is 'x + 1'. 3rd number is 'x + 2'. And 4th number is 'x + 3'. According to the question, 1st number + 2nd number = 4th number. ⇒ x + x + 1 = x + 3 ⇒ x = 2 Putting the value of x we get the numbers 2, 3, 4, and 5. Their LCM is 60 which satisfies the condition in the question. The sum of the four numbers = 2 + 3 + 4 + 5 = 14 Hence, the correct answer is 14.
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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 : If the sum of two numbers is 60 and their HCF and LCM are 5 and 60, respectively, then the sum of the reciprocals of the numbers will be:
Option 1: $\frac{1}{11}$
Option 2: $\frac{1}{6}$
Option 3: $\frac{1}{4}$
Option 4: $\frac{1}{5}$
Question : The product of two numbers is 24 times the difference between these two numbers. If the sum of these numbers is 14, the larger number is:
Option 1: 9
Option 2: 8
Option 3: 7
Option 4: 10
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 2: 105
Option 3: 15
Option 4: 45
Question : The LCM of the two numbers is 44 times their HCF. The sum of the LCM and HCF is 1125. If one number is 25, then the other number is:
Option 1: 1100
Option 2: 975
Option 3: 900
Option 4: 800
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