HCF and LCM – Railway Maths Part IV

Total Questions: 50

1. The LCM of two numbers is 28 times their HCF, and the difference between LCM and HCF is 405. If the numbers are in the ratio 4 : 7, then find the positive difference between the numbers. [Level 5 (15/06/2022) Shift 1]

Correct Answer: (b) 45
Solution:

Let the numbers be 4x and 7x.
Given that, LCM = 28HCF
ATQ, LCM – HCF = 28HCF – HCF = 405
So, HCF = 15 then LCM = 28 × 15
Now, we know that,
LCM × HCF = The product of numbers
⇒ 15 × 28 × 15 = 4x × 7x
⇒ x² = 15 × 15 ⇒ x = 15
So, The difference between the numbers = 3x = 45

2. Find the HCF of 3x²yz, 5xy²z, 12x²y²z³. [Level 5 (15/06/2022) Shift 2]

Correct Answer: (b) xyz
Solution:

H.C.F of 3x²yz , 5xy²z , 12x²y²z³ = xyz

3. The HCF of two different numbers is always 1, when: [Level 5 (15/06/2022) Shift 3]

Correct Answer: (b) Both numbers are prime numbers
Solution:

Two prime numbers have H.C.F always 1.

4. What is the largest number that will divide both 288 and 468 without leaving any remainder? [Level 2 (16/06/2022) Shift 1]

Correct Answer: (b) 36
Solution:

H.C.F of 288 and 468 = 36

5. The number of students in grades 10, 11 and 12 of a school are 384, 256 and 480 respectively. All students were divided into different groups, with no group having students from more than one grade. What is the minimum number of groups that would be formed if all the groups have the same number of students? [Level 2 (16/06/2022) Shift 2]

Correct Answer: (d) 35
Solution:

H.C.F of 384, 256 and 480 = 32

Now,
(384 ÷ 32) + (256 ÷ 32) + (480 ÷ 32)
= 12 + 8 + 15 = 35

6. Find the greatest possible number which on dividing 2307 and 3105 leaves remainders of 7 and 5 respectively. [Level 2 (16/06/2022) Shift 3]

Correct Answer: (d) 100
Solution:

2307 – 7 = 2300 and 3105 – 5 = 3100
H.C.F of 2300 and 3100 = 100

7. Three numbers are in the ratio 17 : 25 : 66 and their HCF is 18. The smallest number among them is: [Level 3 (17/06/2022) Shift 1]

Correct Answer: (c) 306
Solution:

Smallest number = 17 × 18 = 306

8. Let x be the least number lying between 8000 and 8500, which when divided by 12, 14, 16, 35, and 84, the remainders are 4, 6, 8, 27, and 76 respectively. The tens digit in x is: [Level 3 (17/06/2022) Shift 2]

Correct Answer: (a) 9
Solution:

8000 < x < 8500
Divisors = 12, 14, 16, 35, 84
Remainders = 4, 6, 8, 27, 76
Difference between Divisor and Remainder = 8 (constant)

So, Concept used = (LCM of Divisors)k – Difference

Now, LCM (12, 14, 16, 35, 84) = 1680
Here, only possible value of k is 5

Now, 1680k – 8 = 1680 × 5 – 8 = 8392
So, the tens value of x is 9.

9. Kiran has 24 white beads and Resham has 18 black beads. They want to arrange the beads in such a way that each row contains an equal number of beads and each row must contain either only black beads or only white beads. What is the greatest number of beads that can be arranged in a row? [Level 3 (17/06/2022) Shift 2]

Correct Answer: (c) 6  
Solution:

H.C.F of 24 and 18 = 6

10. Ravi has 1530 eggs with him while Vinita has 2380 eggs with her that need to be placed in cartons. What is the maximum number of eggs that each carton should hold so that both Ravi as well as Vinita find such cartons acceptable to use, leaving no empty space, nor having any egg unpacked? [Level 3 (17/06/2022) Shift 3]

Correct Answer: (b) 170
Solution:

H.C.F of 1530 and 2380
1530 = 2 × 3 × 3 × 5 × 17
2380 = 2 × 2 × 5 × 7 × 17
H.C.F = 2 × 5 × 17 = 170