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Math Help - Hcf/lcm

  1. #1
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    Question Hcf/lcm

    How do I find the smallest 4-digit number which is divisible by 18, 24 & 32 using HCF/LCM?

    Thanks,

    Ron
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  2. #2
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    Quote Originally Posted by rn5a View Post
    How do I find the smallest 4-digit number which is divisible by 18, 24 & 32 using HCF/LCM?

    Thanks,

    Ron
    Calculate HCF and LCM.

    LCM will be a three digit number. It can be converted to four digits by multiplying by 10. You can minimize the number, dividing it HCF if possible.
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  3. #3
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    Quote Originally Posted by sa-ri-ga-ma View Post
    Calculate HCF and LCM.

    LCM will be a three digit number. It can be converted to four digits by multiplying by 10. You can minimize the number, dividing it HCF if possible.
    I don't understand why you multiply by 10.

    Let the lcm be called L, it is indeed 3 digits, so take L\cdot\lceil\frac{1000}{L}\rceil. We never need the gcd (aka hcf).
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  4. #4
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    Quote Originally Posted by undefined View Post
    I don't understand why you multiply by 10.

    Let the lcm be called L, it is indeed 3 digits, so take L\cdot\lceil\frac{1000}{L}\rceil. We never need the gcd (aka hcf).
    Hear the LCM has three digits which is divisible by all the three given numbers. But the problem requires smallest 4 digit number divisible by the given numbers. That is why I multiplied by 10 and to make it still smaller, I divided it by HCF
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  5. #5
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    Quote Originally Posted by sa-ri-ga-ma View Post
    Hear the LCM has three digits which is divisible by all the three given numbers. But the problem requires smallest 4 digit number divisible by the given numbers. That is why I multiplied by 10 and to make it still smaller, I divided it by HCF
    Doesn't that give 1440 instead of 1152? Still don't really understand your reasoning. My reasoning is: Disregarding the "smallest 4 digit number" part, the entire solution set is given by k*L where L is the lcm and k is any integer. So find the smallest k such that k*L is 4 digits.
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  6. #6
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    You are right. Thank you.
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