HCF and LCM – (Railway Maths Part VII)

Total Questions: 50

21. The sum and difference of the LCM and HCF of two numbers are 682 and 638 respectively. If the sum of the two numbers is 286, find the numbers. [RRB NTPC 08/04/2021 (Morning) ]

Correct Answer: (b) 220 and 66
Solution:

22. Two numbers are in the ratio of 3:2 and their LCM is 96. Find the numbers. [RRB NTPC 08/04/2021 (Morning) ]

Correct Answer: (c) 48 and 32
Solution:Let the numbers be = 3x and 2x
LCM = 6x = 96 ⇒ x = 16
3 × 16 = 48 and 2 × 16 = 32

23. 391 boys and 323 girls are distributed in groups in such a manner that each group has equal number of members and that the groups have either only boys or only girls. What is the minimum number of groups? [RRB NTPC 08/04/2021 (Evening) ]

Correct Answer: (c) 23
Solution:

24. The ratio of two numbers is 3 : 7 and their HCF is 3. Their LCM is: [RRB NTPC 23/07/2021 (Morning) ]

Correct Answer: (d) 63
Solution:

25. If the HCF of two numbers is 18 and their LCM is 378, then which of the following is a possible pair of such numbers? [RRB NTPC 23/07/2021 (Evening) ]

Correct Answer: (b) 54, 126
Solution:

26. If x + y = 40 and x - y = 20, then the HCF of x and y is: [RRB NTPC 24/07/2021 (Morning) ]

Correct Answer: (d) 10
Solution:

27. Find the HCF of the first 100 natural numbers. [RRB NTPC 24/07/2021 (Evening) ]

Correct Answer: (a) 1
Solution:

The HCF of the first 100 natural numbers is 1.
[ because there are prime numbers 2, 3, 5, ..which can’t have factors other than 1]

28. The GCD of two numbers is 9 and their LCM is 270. If one number is 27, then what will be the second number? [RRB NTPC 24/07/2021 (Evening) ]

Correct Answer: (d) 90
Solution:

29. The smallest number that can be divided exactly by 16, 18, 27, and 45 is: [RRB NTPC 26/07/2021 (Morning) ]

Correct Answer: (b) 2160
Solution:

The LCM of 16, 18, 27, and 45 is = 2160
The smallest number that can be divided exactly by 16, 18, 27, and 45 is 2160.

30. The product of two numbers is 259200 and their LCM is 4320. The HCF of the same two numbers is: [RRB NTPC 26/07/2021 (Morning) ]

Correct Answer: (a) 60
Solution: