HCF & LCM Handout – 1
1.
Find the LCM of 18,25,28,36
a) 1800 b) 6300
c) 2800 d) 3600
2.
Find the least number which is exactly
divisible by 8,12,15,18 and 21.
a)
2520 b) 1720
c) 1260 d) 1800
3.
Find the least number when divided by 12, 25,
30, and 42 leaving no remainder.
a) 1050 b) 4200
c) 2100 d) 1400
4.
LCM of 23×3×52 and 24×52×7 is
a) 24 x3×52×7 b) 23×5
c) 27×3×52x7 d) 212×3×52×7
5.
What is the LCM of 9/5, 27/20 and 54/35
a) 108/35 b) 54
c) 54/35 d) 54/5
6.
What is the LCM of 0.72 , 1.08 , 1.8 and
2.16?
a) 10.8 b) 21.6
c) 108 d) 5.4
7.
The number of integers between 100 and 500,
which are divisible by 3,4 and 5 is
a) 10 b) 9
c) 7 d) 8
8.
LCM of two numbers is 72. The numbers are in
the ratio of 3:4 .The sum of the numbers is
a) 35 b) 38
c) 42 d) 40
9.
Three numbers in the ratio 5:6:8 and their
sum 380. What is their L.C.M.?
a) 1600 b) 1800
c) 1200 d) 2400
10.
If a, and b are relatively prime integers
whose L.C.M. is 868, and if a=31 then b=?
a) 29 b) 28
c)
38 d) 48
11.
The sum of two positive numbers is 63. Their
difference is 1/7 of their sum. What is their LCM?
a) 216 b) 224
c) 108 d) 126
12.
What is the least square number which is
exactly divisible by 7,10,14 and 25?
a) 4900 b) 3600
c) 400 d) 1200
13.
The least number which is a perfect square
and is divisible by each of the numbers 16,20,25, and 35 is
a) 22500 b) 25600
c) 36000 d) 19600
14.
The number of students in a class is a
perfect square, and the total number of students can be divided exactly into
groups of 15, 18, 25, or 30. What is the minimum number of students in the
class?
a) 600 b) 3600
c) 1600 d) 900
15.
Four bells ring at regular intervals of 9,
12, 15, and 18 minutes respectively, starting simultaneously. How long will it
take before they ring together again?
a) 60 min b) 90 min
c) 150
min d) 3 hours
16.
Four traffic lights light at 15 sec., 18
sec., 22 sec., and 36 sec. respectively. If all of them light together at
7:30 a.m. one day, the immediate next time when
they light together is?
a) 8:03
a.m. b) 7:53 a.m.
c) 8:48
a.m. d) 7.58 a.m.
17.
The traffic lights at three different road
crossings change after 24 sec, 36 sec, and 52 sec, respectively. If they all
change simultaneously at 11:32:00 am, then at what immediate time will they
again change
simultaneously?
a) 11:35:54 a.m b) 11:47:36 a.m
c)
12:10:02 p.m d) 11:52:12 a.m
18.
Sameera sets the alarm on two different
clocks. The first alarm rings after every 1 hour 20 minutes and the second
alarm rings after every 1 hour 30 minutes. If both the alarms rang together at
5 a.m., what will be the time when they ring together again immediately?
a) 5 p.m b) 4 p.m
c) 7.30
p.m d) 3 p.m
19.
Five bells commence tolling together and toll
at intervals of 4, 5, 6, 8, and 12 seconds respectively. From 8.00 to 8:30 am,
how many times do they toll together?
a) 4 b) 10
c)
15 d) 16
20.
A rabbit and a dog started running around a
circular ground. The rabbit makes 3 rounds per minute and the dog makes
5 rounds in 2 minutes at regular intervals. If they both starts running
at the same time, how many times do they meet together at the starting point in
each hour?
a) 20 b) 24
c) 30 d) 60
21.
The smallest number which when increased by 7
divided by 12, 15,22, and 28 is_?
a) 2253 b) 4613
c) 4627 d) 2267
22.
What is the least number that when decreased
by 11 is divisible by 18,21,28, and 35?
a) 641 b) 2551
c) 1259 d) 1271
23.
Find the smallest number which when divided
by 8, 12,15, and 21 leaves 7 as the remainder in each case.
a) 413 b) 427
c) 847 d) 833
24.
The least number that when divided by
18,25,36,42 leaving the same remainder of 13 in each case is?
a) 6313 b) 2613
c) 3163 d) 913
25.
The least number which when divided by 7, 8,
12, and 15 leaves a remainder of 3, but when divided by 9 leaves no remainder?
a) 3363 b) 843
c) 2523 d) 1683
26.
Find the least number which when divided by
12, 15, 18, and 21 leaves 5 as a remainder, but when divided by 25 leaves no
remainder.
a) 1265 b) 2525
c) 5010 d) 3025
27.
A gardener was tasked with planting flowers
in rows, each containing an equal number of plants. He attempted to plant 6, 7,
8, and 12 plants per row, but in each case, 5 plants were left over. When he
planted 11 plants per row, none were left over. Find the total number of plants
he has.
a) 173 b) 337
c) 341 d) 509
28.
The smallest number which when divided by 21,
28, 32, and 36 leaves the remainders 17, 24, 28, and 32 respectively is?
a) 1004 b) 2020
c) 2012 d) 2016
29.
The least number when divided by 16, 25,30,
and 42 leaves the respective remainders 11,20,25 and 37 is
a) 8395 b) 8405
c) 4205 d) 4195
30.
Find the greatest number of 4 digits, which
is exactly divisible by 7, 14, 42, and 84.
a) 9980 b) 9964
c) 9946 d) 9996
31.
What is the largest number of 5 digits
divisible by 15, 16,20, and 27?
a) 98840 b) 99360
c) 99230 d) None
32.
The largest number of 5 digits which, when
divided by 15, 24,32, and 36 leaves the same remainder of 10 in each case is
a) 99250 b) 99370
c) 99260 d) 99538
33.
What is the least number of 6 digits which is
exactly divisible by 9, 15,16, and 25?
a) 100800 b) 102800
c) 100200 d) 100260
34.
The number nearest to 12000 which is exactly
divisible by each of 7, 12,14, and 20 is
a) 11890 b) 11760
c) 12240 d) 12180
35.
Let N be the least number of 6 digits which
when divided by 5,6,7,12 and 15 leaves in each case the same remainder 4. What
is the sum of digits of N?
a) 16 b) 15
c) 14 d) 9
