model 2 find lcm of numbers Practice Questions Answers Test with Solutions & More Shortcuts

Question : 26 [SSC CGL Tier-I 2010]

The greatest number, which when subtracted from 5834, gives a number exactly divisible by each of 20, 28, 32 and 35, is

a) 5600

b) 5200

c) 4714

d) 1120

Answer: (c)

220,28,32,35
210,14,16,35
55,7,8,35
71,7,8,7
 1,1,8,1

∴ LCM = 2 × 2 × 5 × 7 × 8 = 1120

∴ Required number

= 5834 – 1120 = 4714

Question : 27 [SSC Constable 2013]

Five bells begin to toll together and toll respectively at intervals of 6, 7, 8, 9 and 12 seconds. After how many seconds will they toll together again ?

a) 318 Sec.

b) 504 Sec.

c) 612 Sec.

d) 72 Sec.

Answer: (b)

Required time = LCM of 6, 7, 8, 9 and 12 seconds

= 504 seconds

Question : 28 [SSC CGL Tier-I 2016]

The LCM of two prime numbers x and y, (x > y) is 161. The value of (3y – x) :

a) 2

b) 1

c) –1

d) –2

Answer: (d)

LCM of x and y = 161

∴ xy = 23 × 7

∴ x = 23; y = 7

∴ 3y – x = 3 × 7 – 23

= 21 – 23 = – 2

Question : 29

Four bells ring at intervals of 4, 6, 8 and 14 seconds. They start ringing simultaneously at 12.00 O’clock. At what time will they again ring simultaneously ?

a) 12 hrs. 3 min. 44 sec.

b) 12 hrs. 3 min. 20 sec.

c) 12 hrs. 3 min.

d) 12 hrs. 2 min. 48 sec.

Answer: (d)

LCM of 4, 6, 8, 14

= 168 seconds

= 2 minutes 48 seconds

They ring again at 12 + 2 min. 48 sec.

= 12 hrs. 2 min. 48 sec.

Question : 30 [SSC CGL Tier-II 2014]

Find the least number which when divided separately by 15, 20, 36 and 48 leaves 3 as remainder in each case.

a) 723

b) 483

c) 243

d) 183

Answer: (a)

Using Rule 4,

i.e. When a number is divided by x, y or z leaving same remainder ‘R’ in each case then that number must be K + R where k is LCM of x, y and z.

Required number = (LCM of 15, 20, 36 and 48) + 3

215,20,36,48
215,10,18,24
315,5,9,12
55,5,3,4
 1,1,3,4

∴ LCM = 2 × 2 × 3 × 5 × 3 × 4 = 720

∴ Required number = 720 + 3 = 723

IMPORTANT quantitative aptitude EXERCISES

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