Home
Class 12
MATHS
There are two numbers a and b whose prod...

There are two numbers a and b whose product is 192 and the quotient of AM by HM of their greatest common divisor and least common multiple is `(169)/(48). The smaller of a and b is

A

2

B

4

C

6

D

12

Text Solution

Verified by Experts

The correct Answer is:
B, D
If G=GED of a and b,L=LCM of a and b, we have `GL=ab=192 " " "……(i)"`
`(AM)/(HM)` of G and L is `((G+L)/(2))((G+L)/(2GL))=(169)/(48)`
`implies (G+L)^(2)=(169)/(12)GL=(169)/(12)GLxx192=13^(2)*4^(2)`
`G+L=52` but `GL=192`
`implies G=4,L=48 implies a=4,b=48` or `a=12,b=16`
Promotional Banner

Similar Questions

Explore conceptually related problems

The HCF of two numbers '11' and 'b' is 5 and their LCM is 200, then the product of 'a' and 'b' is :

If two sets a and b have 99 elements in common then the number of elements common to the sets A x B and B xA is

If the ratio of H.M. and G.M. between two numbers a and b is 4:5 , then the ratio of the two numbers will be

There are two sets A and B each of which consists of three numbers in GP whose product is 64 and R and r are the common ratios such that R=r+2 . If (p)/(q)=(3)/(2) , where p and q are sum of numbers taken two at a time respectively in the two sets. The value of p is

There are two sets A and B each of which consists of three numbers in GP whose product is 64 and R and r are the common ratios such that R=r+2 . If (p)/(q)=(3)/(2) , where p and q are sum of numbers taken two at a time respectively in the two sets. The value of r^(R)+R^(r) is

There are two sets A and B each of which consists of three numbers in GP whose product is 64 and R and r are the common ratios such that R=r+2 . If (p)/(q)=(3)/(2) , where p and q are sum of numbers taken two at a time respectively in the two sets. The value of q is

Find the 10th term of an arithmetic progression whose first term is 'd' and common difference is 'b'.

If A.M and G.M of two positive numbers a and b 10 and 8 respectively , find the numbers ?

Recommended Questions
  1. There are two numbers a and b whose product is 192 and the quotient of...

    Text Solution

    |

  2. दो संख्याओं का लघुत्तम समसवर्त्य उनके महत्तम समापवर्त्य का 12 गुना है।...

    Text Solution

    |

  3. यदि दो संख्याओं का गुणनफल 525 है और उनका महत्तम समापवर्तक 5 है, तो उनक...

    Text Solution

    |

  4. दो संख्याओं का महत्तम समापवर्तक, उनके लघुत्तम समापवर्तक का सदा गुणनखंड...

    Text Solution

    |

  5. क्या यह सही है - दो संख्याओं का महत्तम समापवर्तक 12 है तथा इनका लघुत्...

    Text Solution

    |

  6. दो संख्याओं का लघुत्तम समापवर्तक 1200 है । निम्न संख्याओं में से कौन-स...

    Text Solution

    |

  7. यदि दो संख्याओं के महत्तम समापवर्तक (HCF) तथा लघुत्तम समापवर्तक (LCM) ...

    Text Solution

    |

  8. यदि दो संख्याओ 306 और 657 का महत्तम समापवर्तक 9 हो, तो इनका लघुतम समाप...

    Text Solution

    |

  9. The least common multiple of two numbers is 14 times the greatest comm...

    Text Solution

    |