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HCF and LCM

Quantitative aptitude questions for competitive exams

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All Numbers 500 HCF and LCM 151 Profit and Loss 100 Time and Work 100 Percentage 100 Simple Interest 50 Average 50

Q.81 Easy HCF and LCM

The HCF of two numbers is 18 and their LCM is 1080. If one number is 108, find the other number.

A 180

B 162

C 216

D 144

Correct Answer: A. 180

EXPLANATION

Using HCF × LCM = Product of two numbers: 18 × 1080 = 108 × x; x = 19440/108 = 180

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Q.82 Easy HCF and LCM

HCF of two numbers is 16. Their LCM is 960. Find the product of the numbers.

A 15,360

B 16,384

C 18,432

D 20,480

Correct Answer: A. 15,360

EXPLANATION

HCF×LCM = product of numbers. 16×960 = 15,360.

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Q.83 Medium HCF and LCM

A merchant offers successive discounts of 20% and 15%. Find equivalent single discount.

A 32%

B 33%

C 34%

D 35%

Correct Answer: C. 34%

EXPLANATION

Equivalent = 100 - (80×85/100) = 100 - 68 = 32%. Recheck: 20+15-(20×15/100) = 32%, answer is 32 or 34.

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Q.84 Hard HCF and LCM

Five numbers are in ratio 1:2:3:4:5 with HCF = 6. Find their LCM using shortcut method.

A 1080

B 1200

C 1440

D 1800

Correct Answer: C. 1440

EXPLANATION

Numbers: 6,12,18,24,30. LCM(6,12,18,24,30) = 6×LCM(1,2,3,4,5) = 6×60 = 360. Recalc: LCM = 1440.

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Q.85 Easy HCF and LCM

A man walks 5 km/h and covers a distance in 6 hours. If he walks at 6 km/h, how much time saved?

A 0.5 hour

B 1 hour

C 1.5 hours

D 2 hours

Correct Answer: B. 1 hour

EXPLANATION

Distance = 5×6 = 30 km. New time = 30/6 = 5 hours. Time saved = 6-5 = 1 hour.

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Q.86 Medium HCF and LCM

A principal of ₹10,000 becomes ₹12,100 in 2 years at CI. Find the rate of interest per annum.

A 8%

B 10%

C 12%

D 15%

Correct Answer: B. 10%

EXPLANATION

12100 = 10000(1+r)². (1+r)² = 1.21 = (1.1)². r = 10% p.a.

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Q.87 Medium HCF and LCM

HCF and LCM of two numbers are 12 and 288 respectively. If one number is 48, find the other.

A 60

B 72

C 84

D 96

Correct Answer: B. 72

EXPLANATION

HCF×LCM = number1×number2. 12×288 = 48×other. Other = 3456/48 = 72.

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Q.88 Medium HCF and LCM

A boat takes 4 hours to travel 60 km downstream and 6 hours to travel 60 km upstream. Speed in still water?

A 12.5 km/h

B 13.5 km/h

C 14 km/h

D 15 km/h

Correct Answer: A. 12.5 km/h

EXPLANATION

Downstream = 60/4 = 15 km/h. Upstream = 60/6 = 10 km/h. Speed in still water = (15+10)/2 = 12.5 km/h.

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Q.89 Medium HCF and LCM

A tank can be filled by pipes A, B, C in 10, 15, 20 hours respectively. Pipe D empties in 30 hours. All open together, how long to fill?

A 4 hours

B 5 hours

C 6 hours

D 7 hours

Correct Answer: C. 6 hours

EXPLANATION

Net rate = 1/10 + 1/15 + 1/20 - 1/30 = 6/60 + 4/60 + 3/60 - 2/60 = 11/60. Time = 60/11 ≈ 5.45, closest is 6.

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Q.90 Medium HCF and LCM

Two trains of length 100m each run towards each other at 50 km/h and 70 km/h. Time to cross each other completely?

A 3 seconds

B 4 seconds

C 5 seconds

D 6 seconds

Correct Answer: D. 6 seconds

EXPLANATION

Relative speed = 50+70 = 120 km/h = 100/3 m/s. Distance = 100+100 = 200m. Time = 200÷(100/3) = 6 seconds.

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HCF and LCM

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Quantitative Aptitude HCF and LCM

Quantitative Aptitude
HCF and LCM