HCF and LCM – Railway Maths Part Ⅴ

Total Questions: 48

21. Find the greatest number that divides 128, 303 and 247, leaving remainders 4, 7 and 19, respectively. [RRB NTPC 29/01/2021 (Evening)]

Correct Answer: (a) 4
Solution:

Given numbers are = 128, 303, 247
Remainders = 4, 7, 19
128 − 4 = 124, 303 − 7 = 296,
247 − 19 = 228
HCF of (124, 296, 228) = 4.

22. If the LCM of a and b is c, then their HCF is: [RRB NTPC 29/01/2021 (Evening)]

Correct Answer: (b) ab/c
Solution:

LCM × HCF = Product of two numbers
⇒ c × HCF = a × b
⇒ HCF = (ab) / c

23. What least number should be added to 3500 to make it exactly divisible by 42, 49, 56 and 63? [RRB NTPC 30/01/2021 (Morning)]

Correct Answer: (a) 28
Solution:

LCM of (42, 49, 56, 63) = 3528
Now, 3528 − 3500 = 28
So we should add 28 to 3500.

24. The sum of the two numbers is 850 and their HCF is 25. A possible pair of such numbers is? [RRB NTPC 30/01/2021 (Evening)]

Correct Answer: (a) 225, 625
Solution:

Let, the numbers are = 25X and 25Y
25X + 25Y = 850 ⇒ 25(X + Y) = 850
X + Y = 34 (i.e. 9 + 25 = 34)
So, The possible condition − (25 × 9), (25 × 25) = 225, 625

25. If 288/x and 108/x are natural numbers, then what is the maximum value of x? [RRB NTPC 31/01/2021 (Morning)]

Correct Answer: (d) 36
Solution:

HCF of 288 and 108 = 36
Maximum value of x = 36

26. The HCF of two even numbers should be at least______. [RRB NTPC 31/01/2021 (Morning)]

Correct Answer: (d) 2
Solution:

The HCF of even numbers should be at least 2 because 2 is a factor of all even numbers.

27. HCF and LCM of two numbers are 5 and 210 respectively. If the numbers are between 25 and 40, the sum of the numbers will be: [RRB NTPC 31/01/2021 (Evening)]

Correct Answer: (c) 65
Solution:

HCF = 5
So the number should be multiple of 5
Between 25 and 40 two numbers are multiple of 5 = 30, 35
HCF × LCM = Product of two numbers
⇒ 5 × 210 = 1050
Product of 30 and 35 = 1050
Sum of numbers = 30 + 35 = 65

28. The sum of two numbers is 66 and their HCF and LCM are 3 and 315 respectively. The sum of the reciprocals of the numbers will be: [RRB NTPC 31/01/2021 (Evening)]

Correct Answer: (b) 22/315
Solution:

Let the numbers be x and y
A/Q, x + y = 66
Product of two numbers = HCF × LCM
xy = 3 × 315 = 945
Now, 1/x + 1/y = (x + y) / xy = 66 / 945 = 22 / 315

29. A, B and C begin together to move around in a circular stadium and they complete their revolution in 42 s, 63 s, and 84 s respectively. After how much time they come together at the starting point? [RRB NTPC 02/02/2021 (Morning)]

Correct Answer: (c) 252 s
Solution:

LCM of (42, 63, 84) = 252 sec

30. Q.232. What is the greatest number which divides 13, 26 and 39 and gives the remainders as 1, 2 and 3 respectively? [RRB NTPC 02/02/2021 (Evening)]

Correct Answer: (c) 12
Solution:

HCF of 13, 26 and 39 = 13
Greatest number = 13 − 1 = 12