LCM and HCF


  1. The product of HCF and LCM of 18 and 15 is









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    HCF of 18 and 15
    18 = 2 x 3 x 3
    15 = 3 x 15 = 3
    LCM of 18 and 15 = 2 x 3 x 3 x 5 = 90
    ∴ Product of HCF and LCM of both numbers = 3 x 90 = 270

    Correct Option: D

    HCF of 18 and 15
    18 = 2 x 3 x 3
    15 = 3 x 15 = 3
    LCM of 18 and 15 = 2 x 3 x 3 x 5 = 90
    ∴ Product of HCF and LCM of both numbers = 3 x 90 = 270


  1. The HCF of two numbers is 15 and their LCM is 225. If one of the numbers is 75, then find the another number.









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    Product of LCM and HCF = Product of two numbers

    Correct Option: D

    Let the other number = N
    Product of LCM and HCF = Product of two numbers
    Then, N x 75 = 15 x 225
    ∴ N = (15 x 225)/75 = 45



  1. The HCF of three numbers is 23. If they are in the ratio of 1 : 2 : 3, then find the numbers ?









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    Let the numbers are N, 2N and 3N.
    Where, N = HCF

    Correct Option: B

    Let the numbers are N, 2N and 3N.
    Where, N = HCF
    Given that, N = 23
    ∴ The numbers are 23, 46 and 69.


  1. The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to









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    We have, m x n = 6 x 210 = 1260
    ∴ 1/m + 1/n

    Correct Option: D

    We have, m x n = 6 x 210 = 1260
    ∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35



  1. The ratio of two numbers is 5 : 6 and their LCM is 480, then their HCF is









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    Let numbers are 5N and 6N.
    Now, HCF of these two numbers is N.

    We know that,
    LCM x HCF = Product of two numbers

    Correct Option: B

    Let numbers are 5N and 6N.
    Now, HCF of these two numbers is N.

    We know that,
    LCM x HCF = Product of two numbers
    ⇒ 480 x N = 5N x 6N
    ⇒ 480N = 30N2
    ⇒ N =16