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## Number System: LCM and HCF Test-2

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Question 1 |

The product of two numbers is 15300. What could be the maximum value of their H.C.F.?

45 | |

34 | |

30 | |

42 |

Question 1 Explanation:

Let the two numbers are x and y, and let the HCF of two numbers be f

So the numbers can be written in the form of fx and fy

Now we have the product of two numbers i.e 15300

So we can say that l.c.m. of fx and fy is 15300

So now 15300 = 2

And fx * fy = f

So the maximum value of f

And the maximum value of f = 2x3x5 =30

So the numbers can be written in the form of fx and fy

Now we have the product of two numbers i.e 15300

So we can say that l.c.m. of fx and fy is 15300

So now 15300 = 2

^{2}3^{2}5^{2}17^{1}And fx * fy = f

^{2}xySo the maximum value of f

^{2 }= 2^{2}3^{2}5^{2}And the maximum value of f = 2x3x5 =30

Question 2 |

What will be the LCM of 3/5, 5/15, 4/5, 7/25?

90 | |

84 | |

45 | |

30 |

Question 2 Explanation:

Since we know the LCM of fraction is given by

(LCM of numerator) / (HCF of the denominator)

So we have the LCM OF 3,5,4,7 = 420

HCF ofÂ 5 ,15 ,5, 25= 5

So the LCM of whole fraction is 420/5=84

(LCM of numerator) / (HCF of the denominator)

So we have the LCM OF 3,5,4,7 = 420

HCF ofÂ 5 ,15 ,5, 25= 5

So the LCM of whole fraction is 420/5=84

Question 3 |

Let there are three numbers which are in the ratio of 2:3:4 and the value of their LCM is 948 so what is the smallest of three numbers?

167 | |

168 | |

138 | |

none |

Question 3 Explanation:

Since we have the ratio of three numbers therefore the

three numbers can be written in the form of 2x, 3x, 4x

We have the LCM of the three numbers i.e.948

SoÂ LCMÂ of three numbers 2x,3x,4x = 12x where xÂ is a multiple

So 12x = 948

X = 79

Therefore the smallest number among three isÂ 158, so d is the right answer

three numbers can be written in the form of 2x, 3x, 4x

We have the LCM of the three numbers i.e.948

SoÂ LCMÂ of three numbers 2x,3x,4x = 12x where xÂ is a multiple

So 12x = 948

X = 79

Therefore the smallest number among three isÂ 158, so d is the right answer

Question 4 |

A number is divided by 5,6,7,8 leaves the remainder 4,5,6,7. Which is the smallest such number?

845 | |

678 | |

989 | |

none |

Question 4 Explanation:

The right answer is 839

Since the difference between devisor and the remainder are same so we can say that the number must be the

{(LCM of 5, 6, 7, 8,) â€“ 1} [ 1 is the difference ]

So {lcm of 5,6,7,8}= 840 and the right number is 839

Since the difference between devisor and the remainder are same so we can say that the number must be the

{(LCM of 5, 6, 7, 8,) â€“ 1} [ 1 is the difference ]

So {lcm of 5,6,7,8}= 840 and the right number is 839

Question 5 |

Richa can do a work in 6 days and Meera can do the same work in 8 days. So how many days they will take if they work together?

24/7 | |

23/7 | |

49 | |

48 |

Question 5 Explanation:

Let us assume the total work is ( lcm of 6 and 8 =24)

Now Richa can do 24 units of work in 6 days that means 4 units per day

Meera can do the same work inÂ 8 days that means 3 units per day

Now they both doing the work that means they are dong 7 units per day

So the total time from which they will do the work is 24/7 days i.eÂ option a

Now Richa can do 24 units of work in 6 days that means 4 units per day

Meera can do the same work inÂ 8 days that means 3 units per day

Now they both doing the work that means they are dong 7 units per day

So the total time from which they will do the work is 24/7 days i.eÂ option a

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There are 5 questions to complete.

List |

Q1 answer will 45

15300= 17*2*2*5*5*3*3

And fx * fy = f2xy

So the maximum value of f2

And the maximum value of f = 3x3x5 =45

Fx * fy = f^2xy