LCM and HCF


  1. The smallest number, which when diminished by 3, is divisible by 21, 28, 36 and 45 is ?









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    Required number = (L . C . M of 21, 28, 36, 45 ) + 3

    Correct Option: D

    Required number = (L . C . M of 21, 28, 36, 45 ) + 3
    = (1260 + 3 )
    = 1263


  1. The number of prime factors in 2222 x 3333 x 5555 is ?









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    The number of prime factors in the given product
    = 222 + 333 + 555

    Correct Option: C

    The number of prime factors in the given product
    = (222 + 333 + 555)
    = 1110.



  1. The H.C.F and L.C.M of two number are 44 and 264 respectively. If the first number is divided by 2, the quotient is 44. The other number is ?









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    First number = 2 x 44 = 88
    Second number = (LCM x HCF ) / First number

    Correct Option: C

    First number = 2 x 44 = 88
    Second number = (LCM x HCF ) / First number
    ∴ Second number = 44 x 264 / 88 = 132.


  1. The LCM of two number is 48. The number are in the ratio of 2:3. Find sum of the numbers.









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    Let the numbers be 2x and 3x.
    So, their LCM = 6x
    However, the LCM is given as 48
    ∴ 6x = 48

    Correct Option: C

    Let the numbers be 2x and 3x.
    So, their LCM = 6x
    However, the LCM is given as 48
    ∴ 6x = 48
    ⇒ x=8
    So, the numbers are 16 and 24.
    Hence, their sum is 40.



  1. Find the greatest possible length which can be used to measure 4 m 3 cm, 4 m 34 cm and 4 m 65 cm exactly.









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    Required measure = HCF of 403, 434 and 465 = 31 cm

    Correct Option: A

    Required measure = HCF of 403, 434 and 465 = 31 cm