HCF and LCM – Railway Maths

Total Questions: 50

1. The greatest possible length which can be used to measure exactly the lengths 5 m 25 cm, 7 m 35 cm and 4 m 90 cm is: [Group D 17/08/2022 (Morning)]

Correct Answer: (c) 35 cm
Solution:

Factors of 525, 735, 490 is
5m 25 cm = 525 cm = 5 × 7 × 3 × 5
7m 35 cm = 735 cm = 5 × 3 × 7 × 7
4m 90 cm = 490 cm = 7 × 7 × 5 × 2
Greatest possible length that can be used to measure = HCF of 525, 735, 490 = 5 × 7 = 35 cm

2. If the sum of two numbers is 430 and their HCF is 43, then which of the following is the correct pair? [Group D 17/08/2022 (Morning)]

Correct Answer: (b) 129, 301
Solution:

Check by options
(a) 172, 258 here HCF = 86
(b) 129, 301 here HCF = 43 and sum = 430
(c) 86, 344 here HCF = 86
(d) 215, 215 here HCF = 215

3. The LCM of 48, 72 and another number, x, is 576. Which of the values given below can be the value of x? [Group D 17/08/2022 (Afternoon)]

Correct Answer: (b) 192
Solution:

48 = 2⁴ × 3 and 72 = 2³ × 3²
L.C.M (576) = 2⁶ × 3²
Possible values of x = 2⁶ × 3² , 2⁶ × 3 , 2⁶ = 576, 192, 64
So the value of x as given in options = 192.

4. The HCF of any set of 10 co-prime numbers is always [Group D 18/08/2022 (Morning)]

Correct Answer: (a) 1 
Solution:

The H.C.F of any two co-prime numbers always = 1.

5. Which of the following is the greatest number that divides 72 and 119 and leaves 3 and 4 as respective remainders? [Group D 18/08/2022 (Afternoon)]

Correct Answer: (b) 23
Solution:

72 - 3 = 69 , 119 - 4 = 115
H.C.F of 69 and 115 = 23

6. There are three numbers which are co-prime to one another such that the product of the first two is 357 and that of the last two is 609. What is the sum of the three numbers? [Group D 23/08/2022 (Morning)]

Correct Answer: (b) 67
Solution:

Let the three co-prime numbers be a , b and c.
H.C.F of 357 and 609 = 21
b is common in this two product, b = 21
a = 357 ÷ 21 = 17 and c = 609 ÷ 21 = 29
a + b + c = 17 + 21 + 29 = 67

7. Find the greatest number which will divide 8954, 9806 and 11297 leaving the same remainder in each case. [Group D 23/08/2022 (Evening)]

Correct Answer: (a) 213
Solution:

9806 - 8954 = 852 ,
11297 - 9806 = 1491
and 11297 - 8954 = 2343
H.C.F of 213 and 639 = 213

8. The LCM of two numbers is 84. If the numbers are in the ratio 2 : 3, then find the sum of the numbers. [Group D 24/08/2022 (Morning)]

Correct Answer: (b) 70
Solution:

Let the numbers are 2x and 3x
H.C.F = x and L.C.M = 84
L.C.M × H.C.F = Product of two numbers
⇒ 84x = 6x² ⇒ x = 14
Sum of the numbers = 2x + 3x = 28 + 42 = 70

9. Find the greatest 5-digit number that can be divisible by 18, 15 and 21. [Group D 24/08/2022 (Morning)]

Correct Answer: (d) 99540
Solution:

10. Find the least common multiple (LCM) of 2³ × 3² × 5, 2² × 5² × 7 and 3³ × 5² × 7² [Group D 24/08/2022 (Afternoon)]

Correct Answer: (a) 2³ × 3³ × 5² × 7²
Solution:

2³ × 3² × 5  ,  2² × 5² × 7 and 3³ × 5² × 7²
L.C.M = 2³ × 3³ × 5² × 7²