NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.2 –Part 2

Q-2 Find the LCM and HCF of the following pairs of integers and verify that LCM×HCF=Productofthetwonumbers.

  1. 26 and 91

  2. 510 and 92

  3. 336 and 54

Solution:

  1. 26 and 91

    26=2×13×1 (Expressing as product of prime factors)

    91=7×13×1 (Expressing as product of prime factors)

    Therefore HCFof26and91=13×1=13

    And LCMof26and91=2×7×13×1=182

    Verification:

    LCM×HCF=13×182=2366

    Productof26×91=2366

    Therefore, it is proved that LCM×HCF=Productofthetwonumbers

  2. 510 and 92

    510=2×255

    =2×3×85

    =2×3×5×17

    Therefore 510=2×3×5×17 (Equation A)

    92=2×46

    =2×2×23

    Therefore 92=2×2×23 (Equation B)

    From equation A and B

    HCFof510and92=2

    LCMof510and92=2×2×3×5×17×23=23,460

    Verification:

    LCM×HCF=2×23460=46,920

    Productof510×92=46,920

    Therefore, it is proved that LCM×HCF=Productofthetwonumbers

  3. 336 and 54

    336=2×168

    =2×2×84

    =2×2×2×42

    =2×2×2×2×21

    =2×2×2×2×3×7

    Therefore 336=2×2×2×2×3×7 (Equation A)

    54=2×27

    =2×3×9

    =2×3×3×3

    Therefore 54=2×3×3×3 (Equation B)

    From equation A and B

    HCFof336and54=2×3=6

    LCMof336and54=2×3×2×2×2×7×3×3=24×33×7=3024

    Verification:

    LCM×HCF=6×3024=18144

    Productof336×54=18144

    Therefore, it is proved that LCM×HCF=Productofthetwonumbers

Q-3 Find the LCM and HCF of the following integers by applying the prime factorization method.

  1. 12, 15 and 21

  2. 17, 23 and 29

  3. 8, 9 and 25

Solution:

Given the how to find the LCM and HCF all numbers

Find the LCM and HCF All Numbers

Given the how to find the LCM and HCF all numbers

  1. 12, 15 and 21

    12=2×2×3

    15=5×3

    21=7×3

    From the above, HCF(12,15,21)=3

    And LCM(12,15,21)=3×2×2×5×7=420

  2. 17, 23 and 29

    17=1×17

    23=1×23

    29=1×29

    From the above, HCF(17,23,29)=1

    And LCM(17,23,29)=1×17×23×29=11339

  3. 8, 9 and 25

    8=2×2×2×1

    9=3×3×1

    25=5×5×1

    From the above, HCF(8,9,25)=1

    And LCM(8,9,25)=1×8×9×25=1800

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