#### HCF and LCM Problems Question & Answers

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) 1677 | B) 1683 |

C) 2523 | D) 3363 |

Explanation:

L.C.M of 5, 6, 7, 8 = 840

Required Number is of the form 840k+3.

Least value of k for which (840k+3) is divisible by 9 is k = 2

Required Number = (840 x 2+3)=1683

Subject: HCF and LCM Problems - Quantitative Aptitude - Arithmetic Ability

- Related Questions

A drink vendor has 80 liters of Mazza, 144 liters of Pepsi, and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?

A) 35 | B) 36 |

C) 37 | D) 38 |

Explanation:

If we want to pack the drinks in the least number of cans possible, then each can should contain the maximum numbers of liters possible.As each can contains the same number liters of a drink, the number of liters in each can is a comman factor for 80,144 and 368; and it is also the highest such factor, as we need to store the maximum number of liters in each can.

So, the number of liters in each can = HCF of 80,144 and 368 = 16 liters.

Now, number of cans of Maaza = 80/16 = 5

Number of cans of Pepsi = 144/16 = 9

Number of cans of Sprite = 368/16 = 23

Thus, the total number of cans required = 5 + 9 + 23 = 37

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Subject: HCF and LCM Problems - Quantitative Aptitude - Arithmetic Ability

A room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in Width. Find the least number of square tiles of equal size required to cover the entire floor of the room.

A) 107 | B) 117 |

C) 127 | D) 137 |

Explanation:

Let us calculate both the length and width of the room in centimeters.

Length = 6 meters and 24 centimeters = 624 cm

width = 4 meters and 32 centimeters = 432 cm

As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.

Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 624 and 432 = 48

Thus, the number of square tiles required = (624 x 432 ) / (48 x 48) = 13 x 9 = 117

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Subject: HCF and LCM Problems - Quantitative Aptitude - Arithmetic Ability

The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is

A) 1008 | B) 1015 |

C) 1022 | D) 1032 |

Explanation:

Required Number = (L.C.M of 12, 16, 18,21,28)+7

= 1008 + 7

= 1015

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Subject: HCF and LCM Problems - Quantitative Aptitude - Arithmetic Ability

Find the Greatest Number that will devide 43, 91 and 183 so as to leave the same remainder in each case

A) 4 | B) 7 |

C) 9 | D) 13 |

Explanation:

Required Number = H.C.F of (91- 43), (183- 91) and (183-43)

= H.C.F of 48, 92, and 140 = 4

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Subject: HCF and LCM Problems - Quantitative Aptitude - Arithmetic Ability

A rectangular courtyard 3.78 meters long 5.25 meters wide is to be paved exactly with square tiles, all of the same size. what is the largest size of the tile which could be used for the purpose?

A) 14 cms | B) 21 cms |

C) 42 cms | D) None of these |

Explanation:

3.78 meters =378 cm = 2 × 3 × 3 × 3 × 7

5.25 meters=525 cm = 5 × 5 × 3 × 7

Hence common factors are 3 and 7

Hence LCM = 3 × 7 = 21

Hence largest size of square tiles that can be paved exactly with square tiles is 21 cm.

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Subject: HCF and LCM Problems - Quantitative Aptitude - Arithmetic Ability