PlacementPrepThe HCF of two numbers is 16 and their LCM is 672. If one number is 112, what is the other?
Solution
Product of two numbers = HCF × LCM = 16 × 672 = 10752.
Other number = 10752 ÷ 112 = 96.
Answer: (C) 96
Quantitative Aptitude · Numbers
HCF and LCM: placement practice questions
30 moderate questions in the pattern of campus placement tests. Pick an option to check your answer, then open the step-by-step solution.
Three bells ring at intervals of 9, 16 and 20 minutes. If they ring together at 9:00 a.m., after how many minutes will they next ring together?
Solution
They ring together again after the LCM of 9, 16 and 20.
LCM(9, 16, 20) = 720 minutes.
Answer: (B) 720
What is the least number which, when divided by 9, 12 and 15, leaves remainder 2 in each case?
Solution
LCM of 9, 12 and 15 is 180; it is divisible by all three.
Adding the common remainder: 180 + 2 = 182.
Answer: (B) 182
What is the greatest number that divides 213, 317 and 434 leaving the same remainder 5 in each case?
Solution
Subtract the remainder: 208, 312 and 429.
The HCF of these is 13.
Answer: (B) 13
A room is 660 cm long and 360 cm wide. What is the least number of identical square tiles needed to cover the floor exactly?
Solution
The largest square tile has side equal to the HCF of 660 and 360 = 60 cm.
Tiles = (660 ÷ 60) × (360 ÷ 60) = 11 × 6 = 66.
Answer: (D) 66
What is the LCM of 112 and 98?
Solution
HCF of 112 and 98 is 14.
LCM = (product) ÷ HCF = 112 × 98 ÷ 14 = 784.
Answer: (B) 784
Three bells ring at intervals of 5, 9 and 15 minutes. If they ring together at 9:00 a.m., after how many minutes will they next ring together?
Solution
They ring together again after the LCM of 5, 9 and 15.
LCM(5, 9, 15) = 45 minutes.
Answer: (C) 45
What is the least number which, when divided by 6, 9 and 18, leaves remainder 3 in each case?
Solution
LCM of 6, 9 and 18 is 18; it is divisible by all three.
Adding the common remainder: 18 + 3 = 21.
Answer: (D) 21
What is the greatest number that divides 207, 158 and 53 leaving the same remainder 4 in each case?
Solution
Subtract the remainder: 203, 154 and 49.
The HCF of these is 7.
Answer: (C) 7
A room is 495 cm long and 585 cm wide. What is the least number of identical square tiles needed to cover the floor exactly?
Solution
The largest square tile has side equal to the HCF of 495 and 585 = 45 cm.
Tiles = (495 ÷ 45) × (585 ÷ 45) = 11 × 13 = 143.
Answer: (C) 143
What is the LCM of 28 and 24?
Solution
HCF of 28 and 24 is 4.
LCM = (product) ÷ HCF = 28 × 24 ÷ 4 = 168.
Answer: (D) 168
Three bells ring at intervals of 4, 10 and 12 minutes. If they ring together at 9:00 a.m., after how many minutes will they next ring together?
Solution
They ring together again after the LCM of 4, 10 and 12.
LCM(4, 10, 12) = 60 minutes.
Answer: (D) 60
What is the least number which, when divided by 6, 9 and 18, leaves remainder 2 in each case?
Solution
LCM of 6, 9 and 18 is 18; it is divisible by all three.
Adding the common remainder: 18 + 2 = 20.
Answer: (A) 20
What is the greatest number that divides 443, 477 and 596 leaving the same remainder 1 in each case?
Solution
Subtract the remainder: 442, 476 and 595.
The HCF of these is 17.
Answer: (D) 17
What is the LCM of 98 and 70?
Solution
HCF of 98 and 70 is 14.
LCM = (product) ÷ HCF = 98 × 70 ÷ 14 = 490.
Answer: (B) 490
Three bells ring at intervals of 5, 8 and 9 minutes. If they ring together at 9:00 a.m., after how many minutes will they next ring together?
Solution
They ring together again after the LCM of 5, 8 and 9.
LCM(5, 8, 9) = 360 minutes.
Answer: (B) 360
What is the least number which, when divided by 6, 10 and 16, leaves remainder 1 in each case?
Solution
LCM of 6, 10 and 16 is 240; it is divisible by all three.
Adding the common remainder: 240 + 1 = 241.
Answer: (B) 241
What is the greatest number that divides 134, 239 and 218 leaving the same remainder 1 in each case?
Solution
Subtract the remainder: 133, 238 and 217.
The HCF of these is 7.
Answer: (D) 7
A room is 650 cm long and 150 cm wide. What is the least number of identical square tiles needed to cover the floor exactly?
Solution
The largest square tile has side equal to the HCF of 650 and 150 = 50 cm.
Tiles = (650 ÷ 50) × (150 ÷ 50) = 13 × 3 = 39.
Answer: (A) 39
The HCF of two numbers is 15 and their LCM is 300. If one number is 60, what is the other?
Solution
Product of two numbers = HCF × LCM = 15 × 300 = 4500.
Other number = 4500 ÷ 60 = 75.
Answer: (A) 75
Three bells ring at intervals of 6, 9 and 12 minutes. If they ring together at 9:00 a.m., after how many minutes will they next ring together?
Solution
They ring together again after the LCM of 6, 9 and 12.
LCM(6, 9, 12) = 36 minutes.
Answer: (C) 36
What is the least number which, when divided by 6, 9 and 20, leaves remainder 3 in each case?
Solution
LCM of 6, 9 and 20 is 180; it is divisible by all three.
Adding the common remainder: 180 + 3 = 183.
Answer: (C) 183
What is the greatest number that divides 46, 172 and 165 leaving the same remainder 4 in each case?
Solution
Subtract the remainder: 42, 168 and 161.
The HCF of these is 7.
Answer: (D) 7
A room is 480 cm long and 420 cm wide. What is the least number of identical square tiles needed to cover the floor exactly?
Solution
The largest square tile has side equal to the HCF of 480 and 420 = 60 cm.
Tiles = (480 ÷ 60) × (420 ÷ 60) = 8 × 7 = 56.
Answer: (D) 56
What is the LCM of 72 and 162?
Solution
HCF of 72 and 162 is 18.
LCM = (product) ÷ HCF = 72 × 162 ÷ 18 = 648.
Answer: (A) 648
The HCF of two numbers is 12 and their LCM is 72. If one number is 24, what is the other?
Solution
Product of two numbers = HCF × LCM = 12 × 72 = 864.
Other number = 864 ÷ 24 = 36.
Answer: (D) 36
Three bells ring at intervals of 4, 12 and 20 minutes. If they ring together at 9:00 a.m., after how many minutes will they next ring together?
Solution
They ring together again after the LCM of 4, 12 and 20.
LCM(4, 12, 20) = 60 minutes.
Answer: (C) 60
What is the least number which, when divided by 6, 9 and 16, leaves remainder 1 in each case?
Solution
LCM of 6, 9 and 16 is 144; it is divisible by all three.
Adding the common remainder: 144 + 1 = 145.
Answer: (A) 145
What is the LCM of 75 and 165?
Solution
HCF of 75 and 165 is 15.
LCM = (product) ÷ HCF = 75 × 165 ÷ 15 = 825.
Answer: (B) 825
The HCF of two numbers is 12 and their LCM is 336. If one number is 48, what is the other?
Solution
Product of two numbers = HCF × LCM = 12 × 336 = 4032.
Other number = 4032 ÷ 48 = 84.
Answer: (D) 84
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