Monday, 21 January 2013

Error Analysis #1: HCM & LCM

Find the LCM and HCF of the 3 terms provided.
1. For HCF, should the answer be presented in that manner? If not, how should it be presented?
2. What is wrong with the LCM?


  1. For HCF, the answer is in algebra so instead of b x c you must present it in bc
    For LCM the person missed out the 3 x 5 x 7

  2. for HCF , the answer should not be presented that manner , the answer should be in bc instead of b x c
    for LCM , he missed out the 3 x 5 x 7 and the person also presented wrongly for the answer.

  3. The wrong part of the HCF is the answer is given in an incomplete answer. It should be: bc
    The wrong part of the LCM is the student did not multiply the 5 and 7 in the answer. It should be: 3 x 5 x 7 x b3c4 = 105b3c4

  4. HCF should be presented in bc
    The LCM should include 3,5 and 7

  5. 1. HCF should be presented as a product of 'b' and 'c'. Which would be 'bc'.
    2. LCM does not include the numbers '3', '5' and '7' in the product which would make the equation '3x5x7xa^2xb^3xc^4' It should be presented as '105a^2b^3c^4'

  6. HCF: It is not completely simplified, "b x c" when simplified, is "bc"(the answer)
    LCM: The numbers, "3","5" and "7" were not multiplied together and therefore that is not the lowest common multiple. The correct lowest common multiple is 3x5x7xa^2xb^3xc^4 which is equal to 105a^2b^3c^4.

  7. HCF Mistake:
    bc is already the answer, so the multiplication sign is invalid and will make the structure long-winded.

    LCM Mistake:
    The person forgot to multiply the numbers 3,5 and 7 alongside with the algebra included

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  9. Mistakes
    1. No. It should be simplified to bc instead of b x c.
    2. 3 x 5 x 7 should be added in and a²x b³x c⁴ should be expressed as a²b³c⁴.

  10. 1) No. It should be bc instead of b x c as your answer is not supposed to be in equation form.
    2) 3 x 5 x 7 should be included in the equation and the a²x b³x c⁴ should be expressed as a²b³c⁴ instead of an equation.

  11. 1. No, it should not. The answer should be presented as 'bc' instead of 'bxc' as it it still an algebra equation.
    2. '3x5x7' should be added in as you are to include all of the prime factors to find the lowest common multiple.

  12. 1. The answer is supposed to be in algebra form, so the answer should be 'bc', not 'bxc'.
    2. The LCM is the highest number in every number group in the problem multiplied with each other. Thus, the answer should also include 3x5x7.

  13. 1. b x c equals to b multiplied by c , which should be simplified to bc
    2. To find a LCM from prime factorisation , you have to find the highest number in each set, meaning that 3x5x7 should also be included.

  14. First, the answer for the HCF is not presented properly. It should be presented as 'bc' and not 'b X c'
    Second, when you are finding the LCM, you must also take the uncommon multiples. So in this picture, the person is missing the numbers ' 3, 5, 7'