RRB NTPC LCM AND HCF Questions
Download Top-20 LCM and HCF questions for RRB NTPC exam 2020. Most important LCM and HCF Questions based on asked questions in previous exam papers for RRB NTPC. The following questions are helpful to crack the RRB NTPC Exam 2020.
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Question 1: The H.C.F. and L.C.M. of, two numbers are 8 and 48 respectively. If one of the numbers is 24, then the other number is
a) 48
b) 36
c) 24
d) 16
Question 2: Two numbers are in the ratio 3:4. Their L.C.M. is 84. The greater number is
a) 21
b) 24
c) 28
d) 84
Question 3: The sum of two numbers is 36 and their H.C.F and L.C.M. are 3 and 105 respectively. The sum of the reciprocals of two numbers is
a) 2/35
b) 3/25
c) 4/35
d) 2/25
Question 4: L.C.M. of two numbers is 120 and their H.C.F. is 10. Which of the following can be the sum of those two numbers?
a) 140
b) 80
c) 60
d) 70
Question 5: Product of two coprime numbers is 117. Then their LCM is
a) 9
b) 13
c) 39
d) 117
Question 6: HCF and LCM of two numbers are 11 and 825 respectively. If one number is 275 find the other number.
a) 53
b) 45
c) 33
d) 43
Question 7: What is the LCM (least common multiple) of 57 and 93?
a) 1767
b) 1567
c) 1576
d) 1919
Question 8: What is the HCF (highest common factor) of 57 and 513?
a) 10
b) 57
c) 3
d) 27
Question 9: The two numbers are 63 and 77, HCF is 7, Find the LCM.
a) 668
b) 693
c) 674
d) 680
Question 10: What is the HCF (highest common factor) of 77 and 275?
a) 12
b) 11
c) 7
d) 25
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Question 11: The two numbers are 55 and 99, HCF is 11, What is their LCM?
a) 486
b) 479
c) 476
d) 495
Question 12: What is the HCF (highest common factor) of 133 and 112?
a) 15
b) 7
c) 19
d) 16
Question 13: What is the LCM of 64 and 56?
a) 448
b) 488
c) 484
d) 408
Question 14: The LCM of two numbers is 4 times their HCF. The sum of LCM and HCF is 125. If one of the numbers is 100, then the other number is
a) 5
b) 25
c) 100
d) 125
Question 15: The sum of two numbers is 7 and the sum their squares is 23, their product is equal to:
a) 10
b) 11
c) 12
d) 13
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Question 16: The difference between two numbers is 1146. When we divide the larger number by smaller we get 4 as quotient and 6 as remainder. Find the larger number.
a) 1526
b) 1431
c) 1485
d) 1234
Question 17: The number between 4000 and 5000 that is divisible by each of 12, 18, 21 and 32 is
a) 4302
b) 4032
c) 4023
d) 4203
Question 18: A number between 1000 and 2000 which when divided by 30, 36 & 80 gives a remainder 11 in each case is
a) 1451
b) 1641
c) 1712
d) 1523
Question 19: The product of two numbers is 2160 and their HCF is 12. Numbers of such possible pairs is
a) 1
b) 2
c) 3
d) 4
Question 20: The HCF of two numbers 24 and their LCM is 216. If one of the number is 72, then the other number is
a) 27
b) 72
c) 8
d) 24
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Answers & Solutions:
1) Answer (D)
Given:-
Numbers- First = 24
Second = x (suppose)
H.C.F. of numbers = 8
L.C.M. of numbers = 48
As we know:
H.C.F.* L.C.M. = Product of numbers
Hence
48*8 = 24*x
x = 16
2) Answer (C)
Let the numbers be 3x, 4x
LCM of 3x and 4x is = 12x
So the number 84 is divisible by 12
The numbers are 7×3 = 21 , 7x 4 = 28
The greatest number is 28
3) Answer (C)
let’s say numbers are
hence sum of the reciprocals will be
or
as
and
=
after putting the values we will get summation of reciprocals equals to
4) Answer (D)
We assume that numbers are
So L.C.M. will be =
or
So
or
Hence only option D justifies.
5) Answer (D)
Let the two numbers be a,b.
Hence a * b = L.C.M(a,b) * G.C.D(a,b)
It is given that a,b are co-primes, implies G.C.D(a,b) = 1
Hence from the above equation we get L.C.M(a,b) = a*b = 117
6) Answer (C)
Let the number =
HCF = 11 and LCM = 825
Product of HCF and LCM = Product of the two numbers
=>
=>
=>
=> Ans – (C)
7) Answer (A)
Prime factorization of 57 = 3
Prime factorization of 93 = 3
=> L.C.M. of 57 and 93 = 3
= 57
=> Ans – (A)
8) Answer (B)
Factors of 57 = 1 , 3 , 19 , 57
Factors of 513 = 1 , 3 , 9 , 19 , 27 , 57 , 171 , 513
The common factors are = 1 , 3 , 19 , 57
=> Highest common factor = 57
=> Ans – (B)
9) Answer (B)
H.C.F. (a,b)
The numbers a = 63 and b = 77 and HCF = 7
=> L.C.M. =
=
= 693
10) Answer (B)
Factors of : 77 = 1 , 7 , 11 , 77
275 = 1 , 5 , 11 , 25 , 55 , 275
The common factors are 1 and 11
and HCF = 11
=> Ans – (B)
11) Answer (D)
Let the LCM =
Numbers are = 55 , 99
Also, product of numbers = HCF
=>
=>
=>
=> Ans – (D)
12) Answer (B)
Prime factorization of
133 = 7
112 =
There is only 1 common factor, and thus the HCF (highest common factor) = 7
=> Ans – (B)
13) Answer (A)
(diagram)
so LCM of 64 & 56 is = 8*8*7 = 448
So the answer is option A.
14) Answer (B)
Let one of the numbers =
Let L.C.M =
According to ques, =>
and
Substituting value from equation (i), we get :
=>
=>
Thus, product of numbers =
=>
=>
=> Ans – (B)
15) Answer (D)
Let the numbers be
It is given that
Also,
Squaring both sides, we get :
=>
=>
=>
=>
=> Ans – (D)
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16) Answer (A)
Let the smaller number be
According to ques, on dividing the larger term by smaller one,
=>
=>
=>
=>
=> Ans – (A)
17) Answer (B)
LCM of 12,18,21,32 is 2016
Multiples of 2016 between 4000 and 5000 are 4032.
4032 is present in the options.
Hence, option B is the correct answer.
18) Answer (A)
LCM of given 3 numbers (30, 36, 80) = 720
Multiple of 720 between 1000 and 2000 is 1440.
Hence, option A is the correct answer.
19) Answer (B)
H.C.F. of the two numbers is 12, let the numbers be
Product =
=
=>
Now, factors of 15 = 1, 3, 5, 15
Thus, possible values of
=> Ans – (B)
20) Answer (B)
Let the number be
We know that :
=>
=>
=>
=> Ans – (B)
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