HCF and LCM – Railway Maths Part Ⅴ

Total Questions: 48

31. The LCM of x and y is 2079 and their HCF is 27. If x = 189, what will be the value of y? [RRB NTPC 02/02/2021 (Evening)]

Correct Answer: (d) 297
Solution:

Given, LCM of x and y is 2079 and their HCF is 27
We know that, LCM × HCF = X × Y
2079 × 27 = 189 × Y
⇒ Y = (2079 × 27) / 189 = 297

32. The LCM of √36 and √64 is: [RRB NTPC 03/02/2021 (Morning)]

Correct Answer: (d) 24
Solution:

LCM of √36 and √64 = LCM of 6 and 8 = 24

33. The least number which on being divided by 2, 3, 4, 5 and 6 leaves a remainder of 1 but no remainder when divided by 7 is: [RRB NTPC 03/02/2021 (Evening)]

Correct Answer: (d) 301
Solution:

LCM of (2, 3, 4, 5, 6) = 60
Required number should be divisible by 7
So number will be in the form of 60k + 1
Put k = 5
60 × 5 + 1 = 301
Shortcut − directly check the multiple of 7

34. The sum of two numbers is 72. Their HCF and LCM are 2 and 102, respectively. The sum of the reciprocals of the same two numbers is: [RRB NTPC 04/02/2021 (Morning)]

Correct Answer: (b) 6/17
Solution:

Let, the numbers are A and B
LCM = 102, HCF = 2
A/Q, A + B = 72 ——(i)
and A × B = HCF × LCM
A × B = 2 × 102 ⇒ A × B = 204

The sum of the reciprocals = (1/A) + (1/B)
= (B + A) / (AB) = 72 / 204 = 6 / 17

35. The HCF and LCM of two numbers are 60 and 420, respectively. If the first number is divided by 2, then the quotient is 60. The second number is: [RRB NTPC 04/02/2021 (Morning)]

Correct Answer: (d) 210
Solution:

HCF = 60, LCM = 420
Let, first number = x
Applying Formula, Dividend = Divisor × Quotient + Remainder
A/Q, a = 2 × 60 + 0, a = 120 (1st number)
LCM × HCF = 1st number × 2nd number
420 × 60 = 120 × 2nd number
2nd number = 210

36. 18 apple trees, 21 mango trees and 39 orange trees have to be planted in rows such that each row contains the same number of trees and all of the same variety only. The minimum number of rows in which the trees may be planted is: [RRB NTPC 08/02/2021 (Morning)]

Correct Answer: (a) 26
Solution:

18 apple trees, 21 mango trees and 39 orange trees
Total number of trees = 78
HCF (18, 21, 39) = 3
Now, minimum number of rows = 78 / 3 = 26

37. The product of the LCM and HCF of two positive numbers is 72. The difference of these two numbers is 1. Find the numbers. [RRB NTPC 08/02/2021 (Morning)]

Correct Answer: (d) 8 and 9
Solution:

Let, the numbers are X and Y
Product of the LCM and HCF of two positive numbers is 72 means XY = 72
And X − Y = 1 ——(i)

(X − Y)² = (X + Y)² − 4XY
1 = (X + Y)² − 4 × 72
1 = (X + Y)² − 288
(X + Y)² = 289
X + Y = 17 ——(ii)

From equation (i) and (ii)
X = 8 and Y = 9

38. The HCF and LCM of two numbers are 75 and 450 respectively. If the first number is divided by 3, the quotient is 75. The second number is: [RRB NTPC 08/02/2021 (Morning)]

Correct Answer: (d) 150
Solution:

HCF × LCM = 1st number × 2nd number
———(i)
1st number ÷ 3 = 75
1st number = 75 × 3 = 225
Putting the value of first number in equation (i)
75 × 450 = 225 × 2nd number
Then 2nd number = 150

39. How many of the first 100 positive integers are divisible by 3 or 4 without a remainder? [RRB NTPC 08/02/2021 (Evening)]

Correct Answer: (d) 50
Solution:

Number of integers divisible by 3 = 100 ÷ 3 = 33 (Quotient)

Number of integers divisible by 4 = 100 ÷ 4 = 25
LCM of 3 and 4 = 12
Number of integers divisible by both 3 and 4 = 100 / 12 = 8
Required number of integers = 33 + 25 − 8 = 50

40. The largest number of four digits that is divisible by 12,15 and 18 is: [RRB NTPC 08/02/2021 (Evening)]

Correct Answer: (d) 9900
Solution:

LCM of 12, 15, 18 = 180
Largest number of 4 digit = 9999
The required number must be multiple of 180
When we divide 9999 by 180 we get 99 as remainder
9999 − 99 = 9900