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Homework Help: How to find the hcf and lcm?

  1. Feb 8, 2007 #1
    1. The problem statement, all variables and given/known data
    This is slightly embarassing, but how do you find the hcf and lcm?
    For example, 22,24,30. What would the hcf and lcm be?
    Or,
    The period of f(x)=sinx+cosx is the lcm of 2pi, 2pi, what would that be?


    2. Relevant equations

    HCF*LCM=f(x)*g(x)
     
  2. jcsd
  3. Feb 8, 2007 #2

    Tom Mattson

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    I know what an LCM is, but what's an HCF? Did you perhaps mean GCF?
     
  4. Feb 8, 2007 #3

    HallsofIvy

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    Perhaps that was "Highest" Common Factor. A friend of mine who is not "mathematically" inclined suggested I say "smallest common factor" rather than "least common factor". She said that always made her wonder- what factor is "least common"!

    Chaoseverlasting, in an attempt to reduce some of the chaos, remember that "Least Common Multiple" means the smallest number that is a multiple of each. For example, the least common multiple of 6 and 4 is 12: 12 is 2(6) and 3(4)- it is a multiple of both and is the smallest number that has that property. The least common multiple of 6 and 3, on the other hand, is just 6: 6= 2(3) and 1(6).

    Now, in general, what is the least common multiple of any number, a, and itself. What is the "greatest (or highest) common factor"- that is a number such that each of the given numbers is a multiple of IT- if both numbers are equal?
     
  5. Feb 9, 2007 #4
    Thanks, that helped.
     
  6. Feb 9, 2007 #5
    know anything about euclidean algorithm?

    for HCF I guess you mean highest common factor, which is usually called the GCD, Greatest Common Divisor.

    let's say you want to find GCD of 45 and 12, then
    GCD(45,12)=GCD(45-12,12)=GCD(45-12-12-12,12)=GCD(9,12)=GCD(9,12-9)=GCD(9,3)=GCD(9-3-3-3,3)=GCD(0,3)

    obviously, GCD(45,12)=GCD(0,3)=3

    now, for lcm,
    LCM(a,b)=a*b/GCD(a,b)
     
  7. Feb 10, 2007 #6
    In the UK, HCF is what we use for what in the US you term GCD or GCF.
     
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