Legnagyobb közös osztó (LNKO), legkisebb közös többszörös (LKKT)

Határozd meg a legnagyobb közös osztókat és a legkisebb közös többszörösöket!

1. (90; 420) = ?          [90; 420] = ?

   90 = 2⋅3²⋅5          420 = 2³⋅3⋅5⋅7
   (90; 420) = 2⋅3⋅5 = 30          [90; 420] = 2³⋅3²⋅5⋅7 = 2520

   
   

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2. (528; 792) = ?          [528; 792] = ?

   528 = 2⁴⋅3⋅11          792 = 2³⋅3²⋅11
   (528; 792) = 2³⋅3⋅11 = 264          [528; 792] = 2⁴⋅3²⋅11 = 1584

   
   

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3. (672; 280) = ?          [672; 280] = ?

   672 = 2⁵⋅3⋅7          280 = 2³⋅5⋅7
   (672; 280) = 2³⋅7 = 56          [672; 280] = 2⁵⋅3⋅5⋅7 = 3360

   
   

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4. (780; 1200) = ?          [780; 1200] = ?

   780 = 2²⋅3⋅5⋅13          1200 = 2⁴⋅3⋅5²
   (780; 1200) = 2²⋅3⋅5 = 60          [780; 1200] = 2⁴⋅3⋅5²⋅13 = 15600

   
   

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5. (28800; 2160) = ?          [28800; 2160] = ?

   28800 = 2⁷⋅3²⋅5²          2160 = 2⁴⋅3³⋅5
   (28800; 2160) = 2⁴⋅3²⋅5 = 720          [28800; 2160] = 2⁷⋅3³⋅5² = 86400

   
   

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6. (1050; 1575) = ?          [1050; 1575] = ?

   1050 = 2⋅3⋅5²⋅7          1575 = 3²⋅5²⋅7
   (1050; 1575) = 3⋅5²⋅7 = 525          [1050; 1575] = 2⋅3²⋅5²⋅7 = 3150

   
   

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7. (72000; 21600) = ?          [72000; 21600] = ?

   72000 = 2⁶⋅3²⋅5³          21600 = 2⁵⋅3³⋅5²
   (72000; 21600) = 2⁵⋅3²⋅5² = 7200          [72000; 21600] = 2⁶⋅3³⋅5³ = 216000

   
   

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8. (3696; 1980) = ?          [3696; 1980] = ?

   3696 = 2⁴⋅3⋅7⋅11          1980 = 2²⋅3²⋅5⋅11
   (3696; 1980) = 2²⋅3⋅11 = 132          [3696; 1980] = 2⁴⋅3²⋅5⋅7⋅11 = 55440

   
   

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9. (8910; 264) = ?          [8910; 264] = ?

   8910 = 2⋅3⁴⋅5⋅11          264 = 2³⋅3⋅11
   (8910; 264) = 2⋅3⋅11 = 66          [8910; 264] = 2³⋅3⁴⋅5⋅11 = 35640

   
   

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10. (172800; 576000) = ?          [172800; 576000] = ?

    172800 = 2⁸⋅3³⋅5²          576000 = 2⁹⋅3²⋅5³
    (172800; 576000) = 2⁸⋅3²⋅5² = 57600          [172800; 576000] = 2⁹⋅3³⋅5³ = 1.728.000

    
    

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11. (3600; 27000; 15120) = ?          [3600; 27000; 15120] = ?

    3600 = 2⁴⋅3²⋅5²          27000 = 2³⋅3³⋅5³          15120 = 2⁴⋅3³⋅5⋅7
    (3600; 27000; 15120) = 2³⋅3²⋅5 = 360          [3600; 27000; 15120] = 2⁴⋅3³⋅5³⋅7 = 378000

    
    

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12. (768; 1152) = ?          [768; 1152] = ?

    768 = 2⁸⋅3          1152 = 2⁷⋅3²
    (768; 1152) = 2⁷⋅3 = 384          [768; 1152] = 2⁸⋅3² = 2304

    
    

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13. (10800; 1800) = ?          [10800; 1800] = ?

    10800 = 2⁴⋅3³⋅5²          1800 = 2³⋅3²⋅5²
    (10800; 1800) = 2³⋅3²⋅5² = 1800          [10800; 1800] = 2⁴⋅3³⋅5² = 10800

    
    

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14. (1008; 3360) = ?          [10080; 3360] = ?

    1008 = 2⁴⋅3²⋅7          3360 = 2⁵⋅3⋅5⋅7
    (1008; 3360) = 2⁴⋅3⋅7 = 336          [1008; 3360] = 2⁵⋅5⋅7 = 10080

    
    

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15. (44100; 3960) = ?          [44100; 3960] = ?

    44100 = 2²⋅3²⋅5²⋅7²          3960 = 2³⋅3²⋅5⋅11
    (44100; 3960) = 2²⋅3²⋅5 = 180          [44100; 3960] = 2³⋅3²⋅5²⋅7²⋅11 = 970200

    
    

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