Model 2 Find Lcm Of Numbers Practice Questions Answers Test With Solutions & More Shortcuts

LCM & HCF PRACTICE TEST [5 - EXERCISES]

Model 1 Basic Formula Of LCM & HCF

Model 2 Find Lcm Of Numbers

Model 3 Find Hcf Of Numbers

Model 4 Addition, Subtraction, Multiplication And Division With Lcm & Hcf

Model 5 Lcm & Hcf Vs Ratios

LCM & HCF Important Formulas, Rules, Concepts & Shortcuts

Question : 1 [SSC Section Officer 2007]

The least number, which is a perfect square and is divisible by each of the numbers 16, 20 and 24, is

a) 14400

b) 6400

c) 3600

d) 1600

Answer »

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Answer: (c)

The smallest number divisible by 16, 20 and 24

= LCM of 16, 20 and 24

2	16,	20	24
2	8,	10,	12,
2	4,	5,	6,
	2,	5,	3

∴LCM = 2×2×2×2×5×3

= $2^2$ × $2^2$ × 5 × 3

∴Required complete square number =$2^2$ × $2^2$ × $5^2$ × $3^2$ = 3600

Question : 2 [SSC Investigator 2010]

The smallest number, which, when divided by 12 or 10 or 8, leaves remainder 6 in each case, is

a) 66

b) 126

c) 186

d) 246

Answer »

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Answer: (b)

Using Rule 5,

When a number is divided by P, Q or R leaving remainders X, Y or Z respectively such that the difference between divisor and remainder in each case is same i.e., (P – X) = (Q – Y) = (R – Z) = T (say) then that (least) number must be in the form of (K – T), where K is LCM of P, Q and R

The smallest number divisible by 12 or 10 or 8

= LCM of 12, 10 and 8 = 120

⇒ Required number =120 + 6 = 126

Question : 3

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

a) 3363

b) 2523

c) 1683

d) 1677

Answer »

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Answer: (c)

The LCM of 5, 6, 7 and 8 = 840

∴ Required number = 840 k + 3 which is exactly divisible by 9 for some value of k.

Now, 840 k + 3 = 93 × 9 k + (3k + 3)

When k = 2, 3k + 3 = 9, which is divisible by 9.

∴ Required number = 840 × 2 + 3 = 1683

Question : 4 [SSC CPO 2008]

The smallest number, which when increased by 5 is divisible by each of 24,32, 36 and 564, is

a) 427

b) 4320

c) 859

d) 869

Answer »

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Answer: (c)

Required number = (LCM of 24, 32, 36 and 54) – 5

Now,

2	24,	32,	36,	54
2	12,	16,	18,	27
2	6,	8,	9,	27
3	3,	4,	9,	27
3	1,	4,	3,	9
	1,	4,	1,	3

LCM = 2 × 2 × 2 × 3 × 3 × 3 × 4 = 864

∴ Required number = 864 – 5

= 859

Question : 5

The traffic lights at three different road crossings change after 24 seconds, 36 seconds and 54 seconds respectively. If they all change simultaneously at 10 : 15 : 00 AM, then at what time will they again change simultaneously?

a) 10 : 22 : 12 AM

b) 10 : 17 : 02 AM

c) 10 : 18 : 36 AM

d) 10 : 16 : 54 AM

Answer »

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Answer: (c)

LCM of 24, 36 and 54 seconds

= 216 seconds

= 3 minutes 36 seconds

= 10 : 18 : 36 a.m.

IMPORTANT QUANTITATIVE APTITUDE EXERCISES

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Model 2 Find Lcm Of Numbers Shortcuts »

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LCM & HCF SHORTCUTS AND TECHNIQUES WITH EXAMPLES

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