LCM and HCF

LCM and HCF

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  1. Two numbers are in the ratio 3 : 4. Their L.C.M. is 84. The greater number is








  1. View Hint View Answer Discuss in Forum

    Let the numbers be 3p and 4p.
    ∴ Their LCM = 12p
    ∴ 12p = 84

    ⇒ p =
    84
    		= 7
    12

    Correct Option: C

    Let the numbers be 3p and 4p.
    ∴ Their LCM = 12p
    ∴ 12p = 84

    ⇒ p =
    84
    		= 7
    12

    ∴ Larger number = 4p = 4 × 7 = 28

  1. Two numbers are in the ratio 3 : 4. If their LCM is 240, the smaller of the two number is








  1. View Hint View Answer Discuss in Forum

    Let the number be 3p and 4p. Their LCM = 12p
    According to the question,
    12p = 240

    ⇒ p =
    240
    		= 20
    12

    Correct Option: C

    Let the number be 3p and 4p. Their LCM = 12p
    According to the question,
    12p = 240

    ⇒ p =
    240
    		= 20
    12

    ∴ Smaller number = 3p = 3 × 20 = 60

  1. Three numbers are in the ratio 2 : 3 : 4 and their H.C.F. is 12. The L.C.M. of the numbers is








  1. View Hint View Answer Discuss in Forum

    Let the numbers be 2p, 3p and 4p respectively.
    ∴ HCF = p = 12
    ∴ Numbers are : 2 × 12 = 24 , 3 × 12 = 36, 4 × 12 = 48
    LCM of 24, 36, 48 = 2 × 2 × 2 × 3 × 3 × 2

    Correct Option: A

    Let the numbers be 2p, 3p and 4p respectively.
    ∴ HCF = p = 12
    ∴ Numbers are : 2 × 12 = 24 , 3 × 12 = 36, 4 × 12 = 48
    LCM of 24, 36, 48 = 2 × 2 × 2 × 3 × 3 × 2 = 144

  1. The ratio of two numbers is 4 : 5 and their L.C.M. is 120. The numbers are








  1. View Hint View Answer Discuss in Forum

    Suppose the numbers are 4p and 5p respectively
    According to question
    p × 4 × 5 = 120
    ⇒ p = 6

    Correct Option: C

    Suppose the numbers are 4p and 5p respectively
    According to question
    p × 4 × 5 = 120
    ⇒ p = 6
    ∴ Required numbers = 4p = 4 × 6 = 24 and = 5p = 5 × 6 = 30

  1. If the ratio of two numbers is 2 : 3 and their L.C.M. is 54, then the sum of the two numbers is








  1. View Hint View Answer Discuss in Forum

    Let the two numbers are 2p and 3p respectively.
    According to question,
    LCM = 54
    ⇒ p ( 3 × 2 ) = 54
    ⇒ p = 9
    Numbers = 2p = 2 × 9 = 18 and, 3p = 3 × 9 = 27

    Correct Option: C

    Let the two numbers are 2p and 3p respectively.
    According to question,
    LCM = 54
    ⇒ p ( 3 × 2 ) = 54
    ⇒ p = 9
    Numbers = 2p = 2 × 9 = 18 and, 3p = 3 × 9 = 27
    Sum of the two numbers = 18 + 27 = 45