This is a quiz on the HFC and LCM Questions..

## Quiz- HCF and LCM

There are 13 qeustions with only one correct choice, explanation are provided for answers

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Question 1 |

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

A | 4000 |

B | 3600 |

C | 2400 |

D | 3800 |

Question 1 Explanation:

Factors of 16, 20 and 24 is
16 = 2 ^ 4
20 = 2^ 2 x 5
24 = 2^3 x 3
LCM is 2^4 x 5 x 3 = 240 as is clear to make it a perfect square we need to multiple by 5 and 3 so the power raises to mutiple of 2 so be it. 2^4 x 5^2 x 3^2 = 3600

Question 2 |

What is the minimum number by which I should divide 1875 so that I get a perfect square?

A | 2 |

B | 7 |

C | 5 |

D | 3 |

Question 2 Explanation:

1875 = 625 × 3 = 25 × 25 × 3 = 5 ^ 2 × 3

Question 3 |

In a Birthday celebration, Ram has 3003 Candies and 2730 Toffees, he wants to distribute the sweets in such a way that each of his friend get Same no. Toffee and Candy. How many maximum numbers of friends he can distribute in this way?

A | 153 |

B | 171 |

C | 273 |

D | 173 |

Question 3 Explanation:

Get the max. numbers of factors so that each factor is a prime number then the two numbers can be represented as
3003 - 1001 x 3 = 143 x 7 x 3 = 11 x 13 x 7 x 3
2730 - 910 x 3 = 455 x 2 x 3 = 91 x 5 x 2 x 3 = 13 x 7 x 5 x 2 x 3
HCF - Is 273

Question 4 |

*A,B,C start at the same time in the same direction to run around a circular stadium. A completes a round in 3 min, B in 4 min and C in 6 min, all starting at the same point. How many times they will meet again at the starting point in 36 Min?*

A | 5 |

B | 3 |

C | 4 |

D | 2 |

Question 4 Explanation:

Get the LCM which is 12 divide the 36 by 12 answer is 3. Note since question has asked again it answer is 3 if it has asked after first meet it would be 2

Question 5 |

The least number that should be added to 3446 for it is perfectly divisible by 7, 5 and 3?

A | 105 |

B | 110 |

C | 76 |

D | 96 |

Question 5 Explanation:

The LCM of 7, 5 and 3 is 105. If we divide 3446 with 105 the remainder is 96. 96

Question 6 |

Six bells commence tolling together and toll at intervals at 2,4,6,8,10 and 12 seconds respectively. In 30 min, how many times do they toll together?

A | 15 |

B | 10 |

C | 16 |

D | 14 |

Question 6 Explanation:

L.C.M of 2,4,6,8,10,12 is 120
So, the bells will toll together after every 120 seconds, i.e 2 min
In 30 minutes, they will toll together [(30/2)+1] = 16 times

Question 7 |

The front wheels of a toy tractor are 4 cms in circumference. The back wheels are 7 cms in circumference. If the truck travels in a straight line without slippage, how many inches will the truck have traveled when the front wheels have made 12 more revolutions than the back wheels?

A | 48 |

B | 24 |

C | 64 |

D | 112 |

Question 7 Explanation:

The LCM of 4 and 7 is 28, so the series will have 28, 56, 112 and goes on. On 28, front wheen had 7 revolutions and back wheel has 4 revolutions. The difference is 3. Difference will come to 12 for 112 rev.

Question 8 |

What is HCF of 11.2, 4 , 1.20?

A | 128 |

B | 112 |

C | 28 |

D | 168 |

Question 8 Explanation:

Make the place of decimal as standard in all and then remove decimal. Get the factors and find HCF and then replace decimal
112 = 2^4 x 7
40 = 2^3 x 5
12 = 2^2 x 3
16 x 7 x 5 x 3
168.0

Question 9 |

HCF and LCM of two numbers are 84 and 21.If ratio of two numbers is 1:4.Then largest of two numbers is

A | 22 |

B | 21 |

C | 84 |

D | 42 |

Question 9 Explanation:

If the 2 numbers are a and 4a, then using concept HCF x LCM = a x 4a , 4a^2 = 84 x 21 so a = 21 largest no. is 84

Question 10 |

LCM of two numbers is 48.The numbers are in ratio 2:3. The sum of numbers is

A | 48 |

B | 24 |

C | 40 |

D | 10 |

Question 10 Explanation:

If the numbers are 2a and 3a then LCM is 6a = 48, a = 8 , sum of numbers 16 and 24 is 40

Question 11 |

HCF of a numbers is 41 and the 2 factors of LCM are given a 7 and 3

A | 287 |

B | 124 |

C | 382 |

D | 187 |

Question 11 Explanation:

Just Multiply HCF with max. factor given in LCM in this case 41 x 7

Question 12 |

1095/1168 when expressed in simple form is

A | 13/16 |

B | 17/15 |

C | 15/16 |

D | 11/15 |

Question 12 Explanation:

Get the HCF of 1095 and 1168 and divide both by HCF in this case HCF is 73

Question 13 |

*A,B,C start at the same time in the same direction to run around a circular stadium. A completes a round in 3 min, B in 4 min and C in 6 min, all starting at the same point. After what time will they meet again at the starting point?*

A | 6 Min |

B | 12 Min |

C | 3 Min |

D | 4 Min |

Question 13 Explanation:

Just calculate the LCM.

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