LCM and HCF

LCM and HCF

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  1. What is the um of the digits of the least number which when divided by 54 leaves 35 as remainder, when divided by 80 leaves 61 as remainder and when divided by 119 leaves 100 leaves 100 as remainder ?








  1. View Hint View Answer Discuss in Forum

    (54 - 35) = 19, (80 - 61) = 19 and(119 - 100) = 19
    LCM of 54, 80 and 119 is 257040.
    Required least number = 257040 + 19 = 257059

    Correct Option: D

    (54 - 35) = 19, (80 - 61) = 19 and(119 - 100) = 19
    LCM of 54, 80 and 119 is 257040.
    Required least number = 257040 + 19 = 257059
    Sum of the digits of 257059 = 2 + 5 + 7 + 0 + 5 + 9 = 28

  1. 30 pineapple trees, 45 orange tree and 60 mango trees have to be planted in rows such that each row contains the same number of trees of one variety only. What is minimum number number of row in which the trees may be planted ?








  1. View Hint View Answer Discuss in Forum

    Minimum number of rows = Maximum number of trees in each row
    = HCF of 30,45 and 60

    Correct Option: D

    Minimum number of rows = Maximum number of trees in each row
    = HCF of 30,45 and 60 = 15
    ∴ Number of rows = (30 + 45 + 60)/15 = 9

  1. If HCF of x3 - 10m2 + 31x - 30m and x2 - 8mx + 15 is a linear polynomial, then what is the value of m ?








  1. View Hint View Answer Discuss in Forum

    Go through options, Put m = 1 in two given expression.

    Correct Option: C

    Go through options.
    Put m = 1 in two given expression,we have
    x3 - 10x2 + 31x - 30 and x2 - 8x + 15
    x2 - 8x + 15 = (x - 5) (x - 3)
    x3 - 10x2 + 31x - 30 = (x - 2) (x - 5) (x - 3)
    ∴ (x - 5) (x - 3) = x2 - 8x + 15 is the HCF of both expressions.
    ∴ m = 1

  1. For any integers a and b with HCF (a, b) = 1, what is HCF (a + b, a - b) equal to?








  1. View Hint View Answer Discuss in Forum

    Putting arbitrary values of a and b.

    IIIustration 1:
    Let a = 9 and b = 8
    HCF (8 + 9, 9 - 8)
    HCF (17, 1) = 1

    IIIustration 2:
    Let a = 23 and b =17
    HCF (17 + 23, 23 -17)
    HCF ( 40, 6) = 2

    Hence, HCF (a + b, a - b) can either be 1 or 2.

    Correct Option: C

    Putting arbitrary values of a and b.

    IIIustration 1:
    Let a = 9 and b = 8
    HCF (8 + 9, 9 - 8)
    HCF (17, 1) = 1

    IIIustration 2:
    Let a = 23 and b =17
    HCF (17 + 23, 23 -17)
    HCF ( 40, 6) = 2

    Hence, HCF (a + b, a - b) can either be 1 or 2.

  1. What is the sum of digits of the least number,which when divided by 52 leaves 33 as remainder, when divided by 78 leaves 59 as remainder and when divided by 117 leaves 98 as remainder ?








  1. View Hint View Answer Discuss in Forum

    (52 - 33) = 19, (78 - 59) = 19 and (117 - 98) = 19
    LCM of 52, 78 and 117 is 468.
    Required least number = 468 + 19 = 487

    Correct Option: C

    (52 - 33) = 19, (78 - 59) = 19 and (117 - 98) = 19
    LCM of 52, 78 and 117 is 468.
    Required least number = 468 + 19 = 487
    Sum of digits of 487 = 4 + 8 + 7 = 19