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Arithmetic Ability
Problems On H.C.F And L.C.M
Quiz 3
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Q.1
If the sum of two numbers is 55 and the H.C.F. and L.C.M. of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to:
$$\frac{{55}}{{601}}$$
$$\frac{{601}}{{55}}$$
$$\frac{{11}}{{120}}$$
$$\frac{{120}}{{11}}$$
Q.2
Four bells begin to toll together and toll respectively at intervals of 6, 7, 8 and 9 seconds. In 1.54 hours, how many times do they toll together and in what interval (seconds)?
14, 504
14, 480
12, 504
16, 580
Q.3
The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then the greater number is:
101
107
111
185
Q.4
Three wheels can complete 40, 24 and 16 revolutions per minutes respectively. There is a red spot on each wheel that touches the ground at time zero. After how much time, all these spots will simultaneously touch the ground again ?
$${\text{7}}\frac{1}{2}$$ sec.
18 sec.
$$7\frac{1}{2}$$ min.
18 min.
Q.5
The least number which when divided by 4, 6, 8, 12 and 16 leaves remainder of 2 in each case is = ?
46
48
50
56
Q.6
The LCM of two numbers is 495 and their HCF is 5. If the sum of the numbers is 100, then their difference is = ?
10
46
70
90
Q.7
The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is:
504
536
544
548
Q.8
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is:
12
16
24
48
Q.9
The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
1008
1015
1022
1032
Q.10
The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
1677
1683
2523
3363
Q.11
A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and c in 198 seconds, all starting at the same point. After what time will they again at the starting point ?
26 minutes and 18 seconds
42 minutes and 36 seconds
45 minutes
46 minutes and 12 seconds
Q.12
Find the greatest number of five digits which when divided by 3, 5, 8, 12 leaves 2 as remainder ?
99999
99948
99962
99722
Q.13
A number between 1000 and 2000 which when divided by 30, 36 and 80 gives a remainder 11 in each case is = ?
11523
1451
1641
1712
Q.14
The difference between the greatest and least prime numbers which are less then 100 is = ?
95
96
97
94
Q.15
The number between 4000 and 5000 that is divisible by each of 12, 18, 21 and 32 is = ?
4203
4023
4032
4302
Q.16
Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
40
80
120
200
Q.17
The G.C.D. of 1.08, 0.36 and 0.9 is:
0.03
0.9
0.18
0.108
Q.18
The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
1
2
3
4
Q.19
Let x be the last number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves remainder 0, the sum of digits of x is = ?
24
21
22
18
Q.20
A number when divided by 361 gives remainder 47. When the same number is divided by 19 then find the remainder ?
9
1
8
3
Q.21
Find the HCF of 132, 204 and 228 = ?
12
18
6
21
Q.22
The LCM of four consecutive numbers is 60. The sum of the first two numbers is equal to the fourth number. What is the sum of four numbers
17
14
21
24
Q.23
If the product of three consecutive numbers is 210, then the sum of the smaller numbers is = ?
3
4
5
11
Q.24
Which of the following has most number of divisors?
99
101
176
182
Q.25
The HCF of two numbers is 8. Which one of the following can never be their LCM ?
24
48
56
60
Q.26
252 can be expressed as a product of primes as:
2 × 2 × 3 × 3 × 7
2 × 2 × 2 × 3 × 7
3 × 3 × 3 × 3 × 7
2 × 3 × 3 × 3 × 7
Q.27
An electronic device makes a beep after every 60 sec. Another device makes a beep after every 62 sec. They beeped together at 10 am. The next time, when they would beep together at the earliest is = ?
10.30 am
10.31 am
10.59 am
11 am
Q.28
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes , how many times do they toll together ?
4
10
15
16
Q.29
Three girls start jogging from the same point around a circular track and each one completes one round in 24 seconds, 36 seconds and 48 seconds respectively. After how much time will they meet at one point ?
2 minutes 20 seconds
2 minutes 24 seconds
3 minutes 36 seconds
4 minutes 12 seconds
Q.30
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
4
7
9
13
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