HCF AND LCM OF NUMBERS AND POLYNOMIALS (CDS)

Total Questions: 31

1. HCF of two numbers is 12. Which one of the following can never be their LCM? [2019 (II) Evening Shift ]

Correct Answer: (a) 80
Solution:HCF of two numbers is 12. LCM is common multiple for the two numbers. So, the required answer is 80 because all other are multiple of 12.

2. X Y, and Z start at same point and same time in the same direction to run around a circular stadium. X completes a round in 252 s, Y in 308 s and Z in 198 s. After what time will they meet again at the starting point? [2019 (II) Evening Shift ]

Correct Answer: (d) 46 min 12 s
Solution:X completes round in 252 s.

3. Simplify the question [2019 (II) Evening Shift ]

Correct Answer: (d)
Solution:


4. Solve the following equation [2019 (II) Evening Shift ]

Correct Answer: (a)
Solution:Let p = x³ + 3x² + 3x + 1 = (x  + 1)³

5. The highest four-digit number which is divisible by each of the numbers 16, 36, 45, 48 is [2019 (II) Evening Shift ]

Correct Answer: (b) 9360
Solution:Number which is divisible by 16, 36, 45 and 48 = LCM of (16, 36, 45, 18) LCM of 16, 36, 45, 48 = 720 Now, highest four digit number = 9999

6. Simplify the question [2019 (II) Evening Shift ]

Correct Answer: (c)
Solution:Given, HCF of polynomials = x + 3

7. The product of two integers p and q, where p > 60 and q > 60, is 7168 and their HCF is 16. The sum of these two integers is [2019 (II) Evening Shift ]

Correct Answer: (c) 176
Solution:Given, HCF = 16


8. There are two numbers which are greater than 21 and their LCM and HCF are 3003 and 21 respectively. What is the sum of these numbers? [2018 (I) Morning Shift ]

Correct Answer: (a) 504
Solution:The LCM and HCF of two numbers which are greater than 21 are 3003 and 21 respectively.

9. The product of two non-zero expressions is (x + y + z) p³. If their HCF is p², then their LCM is [2017 (II) Evening Shift ]

Correct Answer: (d) (x + y + z)p
Solution:We know that,
Product of two numbers = LCM of two numbers × HCF of two numbers
∴ (x + y + z)p³ = p² × LCM
LCM = (x + y + z)p

10. Consider the following statements [2017 (I) Morning Shift ]

1. If a = bc with HCF (b,c) = 1, then HCF (c, bd) = HCF (c, d).
2. If a = bc with HCF (b, c) = 1, then LCM (a, d) = LCM (c, bd).

Which of the above statements is / are correct?

Correct Answer: (c) Both 1 and 2
Solution:1. If a = bc with HCF (b, c) = 1