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Math Help - Pre Algebra Question - Finding the LCM of 57 and 63

  1. #1
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    Smile Pre Algebra Question - Finding the LCM of 57 and 63

    Hi

    I am not taking classes or anything, but I want to learn more math and I am basically starting near the bottom. Right now I am working on finding the LCM of a set of numbers and was finding it pretty easy until these two number (57, 63) started giving me problems.

    I am working out of a book and the instructions it gives for finding the LCM are to find the prime factors of each number, underline the most repeated occurence of a number in the factorization and finally to multiply all the numbers together.

    So for 57 I found that the prime factors are: 3 & 19
    And for 63 the prime factors are: 7, 3 & 3

    With the number 57, the numbers 3 and 19 each occur one time. And with 63 the most common occurence is the number 3. So here is what I tried to do...

    3 x 3 x 3 x 19 = LCM 513 (obviously this isnt correct)

    So I checked online and used a LCM calculator and found out that the LCM is actually 1197. The only way I can come up with this number is to multiply 3 x 3 x 7 x 19.

    Can someone help me understand what I am doing wrong? I am afraid it is some simple oversight on my part.

    Thanks
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  2. #2
    MHF Contributor
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    Talking

    When they say "most repeated occurrances" of a factor, I don't think they mean "in each factorization", but "in any one". For instance, 4 and 8 each contain factors of 2, but 8 contains three copies, so that's what you use: three copies of 2. The factorizations of 12 and 18 each contain factors of 2 and 3; 12 contains two copies of 2 and one of 3, while 18 contains one of 2 and two of 3. You use two copies of each, for an LCM of 2*2*3*3 = 36.

    In your case, the one factorization is 3*3*7 and the other is 3*19. You need one 7 (because that's the most that any of the factorizations contains), one 19 (for the same reason), and two 3s. While the one factorization contains only one 3, the other contains two 3s, and you need to include whatever is the maximum number of copies from either of the factorizations.

    For further information, try here.
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  3. #3
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    Thumbs up

    Well that was easy enough. To bad I had to have someone hold my hand and point that out to me.

    Thanks a lot for the help. I understand what I did wrong now!
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  4. #4
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    Simply multiply all prime factors occurring is either number using the highest power.

    Here is an example.
    Suppose that M=2^3\cdot 5^2\cdot 11 and N=2^2\cdot 3^2\cdot 5^3 then LCM(M,N)= 2^3\cdot 3^2\cdot 5^3\cdot 11.
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