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

Question : 36 [SSC CPO 2016]

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?

a) 24

b) 21

c) 14

d) 17

Answer: (c)

260
230
315,
 5

∴ 60 = 2 × 2 × 3 × 5

i.e., Numbers = 2, 3, 4 and 5

∴ Required sum = 2 + 3 + 4 + 5 = 14

Question : 37 [SSC CGL 2011]

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) 18004

b) 18002

c) 18000

d) 17004

Answer: (a)

LCM of 16, 18, 20 and 25 = 3600

∴ Required number = 3600K + 4 which is exactly divisible by 7 for certain value of K.

When K = 5,

number = 3600 × 5 + 4

= 18004 which is exactly divisible by 7.

Question : 38 [SSC CGL Tier-1 2011]

Three bells ring simultaneously at 11a.m. They ring at regular intervals of 20 minutes, 30 minutes, 40 minutes respectively. The time when all the three ring together next is

a) 1.30 p.m.

b) 1.15 p.m.

c) 1 p.m.

d) 2 p.m.

Answer: (c)

LCM of 20, 30 and 40 minutes = 120 minutes

Hence, the bells will toll together again after 2 hours i.e. at 1 p.m.

Question : 39

The number nearest to 10000, which is exactly divisible by each of 3, 4, 5, 6, 7 and 8, is :

a) 10000

b) 9996

c) 10080

d) 9240

Answer: (c)

LCM of 3, 4, 5, 6, 7, 8 = 840

11$760/840$ = 10000

Since, the remainder 760 is more than half of the divisor 840.

∴ The nearest number

= 10000 + (840 – 760) = 10080

Question : 40

A number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves a remainder of 8, and when divided by 8 leaves a remainder of 7, is :

a) 1359

b) 359

c) 539

d) 1539

Answer: (b)

Using Rule 5,

Here, Divisor – remainder = 1

e.g., 10 – 9 = 1, 9 – 8 = 1, 8 – 7 = 1

∴ Required number = (L.C.M. of 10, 9, 8) –1

= 360 – 1 = 359

IMPORTANT quantitative aptitude EXERCISES

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