HCF and LCM – Railway Maths Part III

Total Questions: 52

21. The product of the LCM and the HCF of two numbers is 270. If one of the numbers is 18, find the other number: [Group D 28/09/2022 (Morning)]

Correct Answer: (a) 15
Solution:

Given, L.C.M × H.C.F = 270
L.C.M × H.C.F = product of the two numbers

22. What is the highest common prime factor of 7140 and 13200? [Group D 28/09/2022 (Afternoon)]

Correct Answer: (a) 5 
Solution:

7140 = 3 × 4 × 5 × 7 × 17
13200 = 2 × 2 × 2 × 2 × 3 × 5 × 5 × 11
So, the highest common prime factor is 5.

23. The product of the LCM and the HCF of 18 and 25 is: [Group D 28/09/2022 (Evening)]

Correct Answer: (c) 450
Solution:

We know that,
Product of LCM and HCF = Product of two numbers
Hence,
LCM × HCF = 18 × 25 = 450

24. The HCF of fractions is calculated as [Group D 29/09/2022 (Evening)]

Correct Answer: (c) 1/30​
Solution:

HCF of numerators (2, 4 and 3) = 1
LCM of the denominators (3, 5 and 2) = 30
HCF of 2/3, 4/5 and 3/2 = 1/30

25. Find the HCF of 0.24 and 0.36. [Group D 29/09/2022 (Evening)]

Correct Answer: (b) 0.12
Solution:

HCF of 0.24 and 0.36 = 0.12

26. Four bells toll at intervals of 2, 4, 6 and 8 seconds, respectively. They chimed together at 12 noon. How many times will they chime together in the next 50 minutes, excluding their chiming at 12 noon, but including the one at 12:50 p.m.? [Group D 30/09/2022 (Afternoon)]

Correct Answer: (c) 125
Solution:

LCM of 2, 4, 6 and 8 = 24 sec
Total seconds in 50 min = 3000 sec
Total number of chime = 3000 / 24 = 125

27. The LCM of two numbers is 14 times their HCF. If one of the numbers is 36 and the sum of the LCM and the HCF is 270, then the other number is: [Group D 06/10/2022 (Morning)]

Correct Answer: (a) 126
Solution:

Let their HCF = x and LCM = 14x
According to the question,
14x + x = 270
15x = 270 ⇒ x = 18 ⇒ HCF = 18
LCM = 14x = 14 × 18 = 252

Now,
HCF × LCM = First number × Second number
18 × 252 = 36 × Second number
So, second number = 126

28. The LCM of two numbers is 20 times their HCF and their HCF is 213. If one of the two numbers is divided by 225, the quotient is 4 and the remainder is 165. The other number is: [Group D 06/10/2022 (Afternoon)]

Correct Answer: (b) 852
Solution:

HCF of two numbers = 213
LCM of two numbers = 20 × 213 = 4260
If a number is divided by 225, quotient = 4 and remainder = 165
So, number = 225 × 4 + 165 = 1065
Now,
HCF × LCM = First number × Second number
213 × 4260 = 1065 × Second number
Second number = 852

29. The LCM of two numbers is 10 times their HCF and the sum of the LCM and the HCF is 451. If the sum of the numbers is 287, then one of the two numbers is: [Group D 07/10/2022 (Morning)]

Correct Answer: (a) 82
Solution:

Let the HCF = x and LCM = 10x
According to the question,
x + 10x = 451 ⇒ 11x = 451 ⇒ x = 41
So, HCF = x = 41 and LCM = 10x = 10 × 41 = 410
Sum of numbers = 287
Possible pairs = (41, 246), (82, 205)
But L.C.M. of (41, 246) = 246 ≠ 410
Satisfying pair = (82, 205)
So, one of the numbers = 82

30. If 5 is subtracted from x, then the resulting number is exactly divisible by 18, 16, 24 and 32. The smallest value of x is: [Group D 07/10/2022 (Morning)]

Correct Answer: (a) 293
Solution:

LCM of 18, 16, 24 and 32 = 288
So, number = 288 + 5 = 293