HCF And LCM Applications MCQs

Find the HCF of 408 and 170.

34
17
68
85

Explanation: Using Euclidean algorithm: 408 = 170×2 + 68, 170 = 68×2 + 34, 68 = 34×2 + 0. Hence HCF = 34.

Find the LCM of 72 and 108.

108
216
432
864

Explanation: Prime factors: 72 = 2³×3², 108 = 2²×3³. LCM = 2³×3³ = 8×27 = 216.

Find the HCF of 120, 144 and 180.

6
18
12
24

Explanation: 120 = 2³×3×5, 144 = 2⁴×3², 180 = 2²×3²×5. HCF = 2²×3 = 12.

Find the LCM of 15, 25 and 35.

175
350
875
525

Explanation: 15 = 3×5, 25 = 5², 35 = 5×7. LCM = 3×5²×7 = 525.

If HCF of 56 and 72 is 8, what is their LCM?

504
2016
6048
8064

Explanation: Product = HCF × LCM. So LCM = (56×72)/8 = 4032/8 = 504.

Find the HCF of 1001 and 847.

7
77
11
91

Explanation: 1001 - 847 = 154. HCF(847, 154): 847 = 154×5 + 77, 154 = 77×2 + 0. HCF = 77.

A rectangular floor measures 360 cm × 240 cm. What is the largest square tile that can exactly fit?

60 cm
80 cm
120 cm
180 cm

Explanation: Largest square tile = HCF(360, 240) = 120 cm.

How many 40 cm × 40 cm tiles are needed to cover a 360 cm × 240 cm floor exactly?

27
108
64
54

Explanation: Area = 86400, Tile area = 1600. Number = 86400/1600 = 54.

Three bells toll at intervals of 6, 8 and 12 seconds. When will they next toll together?

24 seconds
16 seconds
48 seconds
72 seconds

Explanation: LCM(6, 8, 12) = 24. They toll together every 24 seconds.

Four runners complete a circular track in 15, 20, 30 and 45 seconds. When do they all meet at the start?

60 seconds
180 seconds
90 seconds
300 seconds

Explanation: LCM(15, 20, 30, 45) = 180 seconds.

Find the largest number that divides 200, 320 and 440 leaving the same remainder each time.

40
80
120
240

Explanation: If remainder is r, then n divides (320-200)=120, (440-320)=120, (440-200)=240. HCF(120,120,240) = 120.

Find the smallest number which when divided by 3, 4, 5 leaves remainders 2, 3, 4 respectively.

57
60
119
59

Explanation: x+1 is divisible by 3, 4, 5. LCM(3,4,5) = 60. So x = 60-1 = 59.

How many pairs of numbers less than 100 have HCF exactly equal to 12?

14
12
16
18

Explanation: Numbers are 12a, 12b where a,b are co-prime and 12a, 12b < 100. Counting valid pairs gives 14.

What is the HCF of 17 and 23?

0
1
17
391

Explanation: 17 and 23 are co-prime (both prime). HCF = 1.

What is the LCM of 17 and 23?

1
40
391
24

Explanation: For co-prime numbers, LCM = product = 17×23 = 391.

What is the HCF of 2/3 and 4/5?

4/15
1/5
1/15
2/15

Explanation: HCF of fractions = HCF(2,4)/LCM(3,5) = 2/15 = 2/15.

What is the LCM of 2/3 and 4/5?

4
4/15
8/15
2/5

Explanation: LCM of fractions = LCM(2,4)/HCF(3,5) = 4/1 = 4.

Two numbers have product 2160 and HCF 12. If one number is 36, what is the other?

48
60
72
108

Explanation: If HCF is 12, numbers are 12a and 12b. Product = 144ab = 2160, so ab = 15. If one is 36 = 12×3, other = 12×5 = 60.

What is the remainder when 84 and 144 are divided by their HCF?

6
24
0
36

Explanation: HCF(84,144) = 12. By definition, HCF divides both numbers exactly, so remainder is 0.

Three vessels contain 120, 180 and 240 litres of milk. What is the largest exact measuring container to empty all?

30 litres
90 litres
120 litres
60 litres

Explanation: HCF(120,180,240) = 60 litres. This is the largest container that measures each exactly.

What is the smallest number divisible by 12, 15 and 18?

180
90
360
540

Explanation: LCM(12,15,18) = 180.

Find the least number of students that can be arranged in rows of 12, 15 or 18 with no remainder.

90
180
360
540

Explanation: LCM(12,15,18) = 180.

What is the HCF of 1.20, 2.40 and 3.60?

0.60
2.40
1.20
3.60

Explanation: Convert to integers: 120, 240, 360. HCF = 120. Divide by 100: 1.20.

What is the LCM of 0.5, 1.5 and 2.5?

2.5
5.0
7.5
12.5

Explanation: Convert to integers: 5, 15, 25. LCM = 75. Divide by 10: 7.5.

What is the HCF of 6x²y and 8xy³?

2xy
2x²y
2xy³
4x²y³

Explanation: HCF of coefficients 6 and 8 is 2. For variables, take lowest power: x¹ and y¹. HCF = 2xy.

What is the LCM of 6x²y and 8xy³?

24x²y
24x²y³
24xy³
48x²y³

Explanation: LCM of coefficients 6 and 8 is 24. For variables, take highest power: x² and y³. LCM = 24x²y³.

Find the number between 200 and 300 divisible by 6, 8 and 10.

200
280
240
300

Explanation: LCM(6,8,10) = 120. Multiples: 120, 240, 360... Only 240 is between 200 and 300.

Find the greatest number that divides 1850 and 2320 leaving remainders 5 and 7 respectively.

3
41
123
9

Explanation: Number divides 1850-5=1845 and 2320-7=2313. HCF(1845,2313) = 9.

Find the smallest number which when divided by 4, 5, 6 leaves remainders 3, 4, 5 respectively.

59
57
60
119

Explanation: x+1 is divisible by 4, 5, 6. LCM(4,5,6) = 60. So x = 60-1 = 59.

Two numbers have sum 120 and HCF 15. What is their maximum possible product?

1575
3375
2250
4500

Explanation: Numbers are 15a and 15b where a+b = 8 and a,b co-prime. Pairs: (15,105) product 1575, (45,75) product 3375. Maximum is 3375.

Three traffic lights change at intervals of 30, 45 and 60 seconds. If they change together at 8:00 AM, when next together?

90 seconds
120 seconds
180 seconds
240 seconds

Explanation: LCM(30,45,60) = 180 seconds. They next change together after 180 seconds = 3 minutes.

Find the HCF of 1260 and 1386.

18
42
63
126

Explanation: 1260 = 2²×3²×5×7, 1386 = 2×3²×7×11. HCF = 2×3²×7 = 126.

Find the LCM of 1260 and 1386.

13860
6930
27720
41580

Explanation: 1260 = 2²×3²×5×7, 1386 = 2×3²×7×11. LCM = 2²×3²×5×7×11 = 13860.

Two numbers have HCF 18 and sum 126. For the pair with maximum product, what is the difference between the numbers?

36
18
54
72

Explanation: Numbers are 18a and 18b where a+b = 7. Pairs: (18,108) product 1944, (36,90) product 3240, (54,72) product 3888. Maximum product pair is (54,72), difference = 72-54 = 18.

What is the LCM of 11, 13 and 17?

2331
2531
2431
4862

Explanation: Since 11, 13, 17 are pairwise co-prime, LCM = 11×13×17 = 2431.

What is the HCF of 47 and 48?

0
47
48
1

Explanation: Consecutive integers are always co-prime. HCF = 1.

What is the LCM of 47 and 48?

2256
47
48
1128

Explanation: Since consecutive integers are co-prime, LCM = 47×48 = 2256.

What is the LCM of 31 and 37?

1
1147
68
1146

Explanation: Both are prime, so co-prime. LCM = 31×37 = 1147.

Two ropes of lengths 84m and 126m are to be cut into equal pieces of maximum length. How many pieces total?

3
7
5
10

Explanation: Maximum length = HCF(84,126) = 42m. Pieces = 84/42 + 126/42 = 2 + 3 = 5.

Buses from a station depart at intervals of 20, 30 and 45 minutes. If they depart together at 6:00 AM, when next together?

90 minutes
120 minutes
240 minutes
180 minutes

Explanation: LCM(20,30,45) = 180 minutes = 3 hours. Next together at 9:00 AM.

168 students, 252 books and 336 pens are to be distributed equally. What is the maximum number of students possible?

84
72
96
168

Explanation: Maximum students = HCF(168,252,336) = 84. Each gets 2 books and 4 pens.

Find the smallest number which when divided by 2, 3, 4, 5 leaves remainders 1, 2, 3, 4 respectively.

56
59
60
119

Explanation: x+1 is divisible by 2, 3, 4, 5. LCM(2,3,4,5) = 60. So x = 60-1 = 59.

Three numbers are in ratio 3:4:5 and their LCM is 240. What is their HCF?

8
12
4
20

Explanation: Numbers are 3x, 4x, 5x. LCM = x×LCM(3,4,5) = 60x = 240, so x = 4. Numbers: 12, 16, 20. HCF = 4.

Three numbers are in ratio 2:3:4 and their HCF is 12. What is their LCM?

72
288
576
144

Explanation: Numbers are 24, 36, 48. LCM(24,36,48) = 144.

The HCF of two numbers is 12 and their LCM is 360. If one number is 72, what is the other?

60
48
72
84

Explanation: Product of numbers = HCF × LCM = 12×360 = 4320. Other number = 4320/72 = 60.

Find the largest number that divides 200, 320 and 440 leaving the same remainder in each case.

40
120
80
240

Explanation: Number divides differences: 120, 120, 240. HCF = 120.

Three alarms ring at intervals of 15, 20 and 30 minutes starting at 8:00 AM, 8:10 AM and 8:20 AM respectively. When do they first ring together?

9:00 AM
10:00 AM
9:30 AM
10:30 AM

Explanation: A rings at 8:00, 8:15, 8:30, 8:45, 9:00, 9:15, 9:30... B at 8:10, 8:30, 8:50, 9:10, 9:30... C at 8:20, 8:50, 9:20, 9:50... First common time is 9:30 AM (90 minutes after 8:00).

What is the HCF of x²-4 and x²-5x+6?

x+2
x-3
(x-2)(x+2)(x-3)
x-2

Explanation: x²-4 = (x-2)(x+2), x²-5x+6 = (x-2)(x-3). Common factor is (x-2).

What is the LCM of x²-4 and x²-5x+6?

(x-2)(x+2)(x-3)
(x-2)(x+2)
(x-2)(x-3)
(x+2)(x-3)

Explanation: x²-4 = (x-2)(x+2), x²-5x+6 = (x-2)(x-3). LCM = (x-2)(x+2)(x-3).

How many ordered pairs of positive integers have LCM exactly equal to 30?

10
14
12
16

Explanation: Pairs: (1,30), (2,15), (2,30), (3,10), (3,30), (5,6), (5,30), (6,10), (6,15), (6,30), (10,15), (10,30), (15,30), (30,30). Total = 14.

What is the HCF of 8! and 9!?

24
12
48
96

Explanation: HCF(72+48, 72-48) = HCF(120, 24) = 24.

What is the LCM of 8! and 9!?

40320
181440
725760
362880

Explanation: 9! = 9×8!. LCM(8!, 9!) = 9! = 362880.

What is the HCF of 72+48 and 72-48?

24
12
48
96

Explanation: HCF(72+48, 72-48) = HCF(120, 24) = 24.

What is the HCF of 2⁶ and 2⁸?

32
64
128
256

Explanation: HCF(2⁶, 2⁸) = 2^min(6,8) = 2⁶ = 64.

What is the LCM of 2⁶ and 2⁸?

64
128
256
512

Explanation: LCM(2⁶, 2⁸) = 2^max(6,8) = 2⁸ = 256.

What is the HCF of 48 and 50?

1
24
25
2

Explanation: 48 = 2×24, 50 = 2×25. HCF(24,25) = 1, so HCF(48,50) = 2.

What is the LCM of 48 and 50?

1200
600
2400
4800

Explanation: 48 = 2×24, 50 = 2×25. LCM = 2×LCM(24,25) = 2×24×25 = 1200.

What is the HCF of 17 and 51?

1
17
3
51

Explanation: Since 51 = 3×17, HCF(17,51) = 17.

What is the LCM of 17 and 51?

17
34
51
867

Explanation: Since 51 = 3×17, LCM(17,51) = 51.

A room measures 72 inches × 48 inches. What is the minimum number of identical square tiles needed to cover the floor (without cutting)?

3
12
18
6

Explanation: Largest square tile = HCF(72,48) = 24 inches. Number of tiles = (72×48)/(24×24) = 3×2 = 6.

HCF And LCM Applications Practice

Performance Summary

Choose a Topic to Start Practice

Daily Current Affairs