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Thread: Applications of LCM & HCF concept

  1. #1
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    I know how to calculate LCM & HCF. I am looking for Questions that do not expliclity say find the LCM or HCF, but require the use of this concept to solve the question. Usually such Question are word problems. Can anyone help with examples and also tell the answers so that I can verify my understanding of the concept.

    Thanks

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    anupam try this one

    There are 2 persons A & B running in a cricle, A completes one revolution in 4 min and B completes one revolution in 7 min. They start running togather, after how much time A & B will meet at starting point. (Assume any missing information)

    a) They move in opposite directions
    b) They move in same direction.

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    I tried the same direction problem, with the answer being 28 minutes, but I am not clear as to how will the answer and why will it be different if they were moving in opp direction?

    Pnakaj or anybody else?



    Originally posted by pankajagg

    anupam try this one

    There are 2 persons A & B running in a cricle, A completes one revolution in 4 min and B completes one revolution in 7 min. They start running togather, after how much time A & B will meet at starting point. (Assume any missing information)

    a) They move in opposite directions
    b) They move in same direction.

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    Answer will not be different, even if they are moving in opp direction

    A completes one round in 4 min and this is irrespective of B's revolution
    B completes its revolution in 7 min in any direction so the answer will be the same

    Had the question been when will they first meet then directions would have matter

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    I found another LCM application problem

    The front wheels of a toy truck are 4 inches in circumference. The back wheels are 7 inches 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) 112 (B) 64 (C) 48 (D) 36 (E) 28


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    Ans is 112.

    Answer should be multiples of 4 and 7. so it is 28, 56, 112.....and so on
    suppose if we choose 28, 56, and 112 then

    4 will take (28/4) 7 revolution and 7 will take (7/28) 4 revolutions and the difference is (4-7) 3....but we are looking for difference of 12.

    4 will take (56/4) 14 revolution and 7 will take (56/7) 8 so the difference is (14-7) 7...which doesnt clik

    4 will take (112/4) 28 and 7 will take (112/7) 16 and difference is 12 which is the correct.

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    Option (A) 112 is correct


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    Two methods for the 4' and 7' wheel solution

    Method1: HCF = 28 => 4X28=112
    Method2:
    D=7n=4(n+12)
    7n=4n+48
    3n=48
    n=16
    D=7x16=4(16+12)=112 inches

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    @PeterAbhraham

    @peterabraham: The one you are quoting should be LCM

    LCM is 28.
    HCF is 1 because 4 and 7 are relatively prime to each other
    .

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    Oops. It is L.C.M. Thanks.
    Quote Originally Posted by peterabraham View Post
    Method1: HCF = 28 => 4X28=112
    Method2:
    D=7n=4(n+12)
    7n=4n+48
    3n=48
    n=16
    D=7x16=4(16+12)=112 inches

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