HCF & LCM MCQs for Competitive Examination
Solve the following problems.
Q. 21
The greatest number of four digits which when divided by 3, 5, 7, 9 leave remainders 1, 3, 5, 7 respectively is
(A) 9763
(B) 9764
(C) 9766
(D) 9765
Answer: (A) 9763
Explanation: N/A
Q. 22
The least number which when divided by 16, 18, 20 and 25 leaves 4 as remainder in each case but when divided by 7 leaves no remainder is
(A) 17004
(B) 18000
(C) 18002
(D) 18004
Answer: (D) 18004
Explanation: N/A
Q. 23
The traffic lights at three different road crossings change after 24 seconds, 36 seconds and 54 seconds respectively. If they all change simultaneously at 10.15 a.m., then at what time will they again change simultaneously?
(A) 10 : 16 : 54 a.m.
(B) 10 : 18 : 36 a.m.
(C) 10 : 17 : 02 a.m.
(D) 10 : 22 : 12 a.m.
Answer: (B) 10 : 18 : 36 a.m.
Explanation: N/A
Q. 24
Four runners started running simultaneously from a point on a circular track. They took 200 seconds, 300 seconds, 360 seconds and 450 seconds to complete one round. After how much time do they meet at the starting point for the first time?
(A) 1800 seconds
(B) 3600 seconds
(C) 2400 seconds
(D) 4800 seconds
Answer: (A) 1800 seconds
Explanation N/A
Q. 25
The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35 is
(A) 1120
(B) 4714
(C) 5200
(D) 5600
Answer: (B) 4714
Explanation: N/A
Q. 26
If the students of a class can be grouped exactly into 6 or 8 or 10, then the minimum number of students in the class must be
(A) 60
(B) 120
(C) 180
(D) 240
Answer: (B) 120
Explanation: N/A
Q. 27
The greatest number that will divide 729 and 901 leaving remainders 9 and 5 respectively is
(A) 15
(B) 16
(C) 19
(D) 20
Answer: (B) 16
Explanation: The required number = HCF(729 – 9, 901 – 5) = HCF(720, 896) = 16
Q. 28
Find the greatest number which will exactly divide 200 and 320.
(A) 10
(B) 20
(C) 16
(D) 40
Answer: (D) 40
Explanation: N/A
Q. 29
Three sets of English, Mathematics and Science books containing 336, 240, 96 books respectively have to be stacked in such a way that all the books are stored subject-wise and the height of each stack is the same. The total number of stacks will be
(A) 14
(B) 21
(C) 22
(D) 48
Answer: (A) 14
Explanation: Number of books in each stack = HCF(336, 240, 96) = 48
Total stacks = (336 + 240 + 96)/48 = 14
Q. 30
Find the number of pair of positive integers whose sum is 99 and HCF is 9.
(A) 2
(B) 3
(C) 4
(D) 5
Answer: (D) 5
Explanation: N/A
Q. 31
The sum of two numbers is 36 and their HCF and LCM are 3 and 105 respectively. The sum of the reciprocal of two numbers is
(A) 2/25
(B) 3/35
(C) 4/35
(D) 2/25
Answer: (C) 4/35
Explanation: Let the two numbers be x and y
then xy = 3 * 105 = 315
and x + y = 36 (given)
hence (x + y)/xy =36/315
or (1/x) + (1/y) = 4/35
Q. 32
Let x be the smallest number, which when added to 2000 makes the resulting number divisible by 12, 16, 18 and 21. The sum of the digits of x is
(A) 7
(B) 5
(C) 6
(D) 4
Answer: (A) 7
Explanation: LCM(12, 16, 18, 21) = 1008
1008 * 2 = 2016 = 2000 + 16
x = 16
Sum of digits of 16 = 1 + 6 = 7
Q. 33
The greatest four-digit number which is exactly divisible by each one of the numbers 12, 18, 21 and 28 is
(A) 9828
(B) 9288
(C) 9882
(D) 9928
Answer: (A) 9828
Explanation: N/A
Q. 34
A number x is divisible by 7. When this number is divided by 8, 12 and 16 it leaves a remainder 3 in each case. The least value of x is
(A) 148
(B) 149
(C) 150
(D) 147
Answer: (D) 147
Explanation: N/A
Q. 35
The smallest five-digit number which is divisible by 12, 18 and 21 is
(A) 10224
(B) 30256
(C) 10080
(D) 50321
Answer: (C) 10080
Explanation: N/A
Q. 36
A number between 1000 and 2000 which when divided by 30, 36 and 80 gives a remainder 11 in each case is
(A) 1451
(B) 1641
(C) 1712
(D) 1523
Answer: (A) 1451
Explanation: N/A
Q. 37
The number between 4000 and 5000 that is divisible by each of 12, 18, 21 and 32 is
(A) 4023
(B) 4032
(C) 4302
(D) 4203
Answer: (B) 4032
Explanation: N/A
Q. 38
If x : y be the ratio of two whole numbers and z be their HCF, then the LCM of those two numbers is
(A) yz
(B) xz/y
(C) xy/z
(D) xyz
Answer: (D) xyz
Explanation: Ratio of the number = x : y and HCF of the two numbers = z
Let the two numbers be xz and yz
Product of the two numbers = LCM * HCF
or, LCM = (xz * yz)/z = xyz
Q. 39
Three numbers are in the ratio 1 : 2 : 3 and their HCF is 12. The numbers are
(A) 12, 24, 36
(B) 5, 10, 15
(C) 4, 8, 12
(D) 10, 20, 30
Answer: (A) 12, 24, 36
Explanation: N/A
Q. 40
The HCF and LCM of two numbers are 21 and 84 respectively. If the ratio of the two numbers is 1 : 4, then the largest of the two numbers is
(A) 12
(B) 108
(C) 48
(D) 84
Answer: (D) 84
Explanation: N/A