Ejercicio 116

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CAPITULO XII

Mínimo Común Múltiplo
Ejercicio 116
Hallar el m.c.m de:
  1. 2a,4x8 2a 4x8= 2 2 (x2 ) m.c.m= 2 2 a(x2 ) m.c.m=4a(x2 )
  2. 3 b 2 ,ab b 2 3 b 2 ab b 2 =b(ab ) m.c.m=3 b 2 (ab )
  3. x 2 y, x 2 y+x y 2 x 2 y x 2 y+x y 2 =xy(x+y ) m.c.m= x 2 y(x+y )
  4. 8,4+8a 8= 2 3 4+8a= 2 2 (1+2a ) m.c.m= 2 3 (1+2a ) m.c.m=8(1+2a )
  5. 6 a 2 b,3 a 2 b 2 +6a b 3 6 a 2 b=2.3 a 2 b 3 a 2 b 2 +6a b 3 =3a b 2 (a+2b ) m.c.m=2.3 a 2 b 2 (a+2b ) m.c.m=6 a 2 b 2 (a+2b )
  6. 14 x 2 ,6 x 2 +4xy 14 x 2 =2.7 x 2 6 x 2 +4xy=2x(3x+2y ) m.c.m=2.7 x 2 (3x+2y ) m.c.m=14 x 2 (3x+2y )
  7. 9m,6m n 2 12mn 9m= 3 2 m 6m n 2 12mn=6mn(n2 ) =2.3mn(n2 ) m.c.m=2. 3 2 mn(n2 ) m.c.m=18mn(n2 )
  8. 15,3x+6 15=3.5 3x+6=3(x+2 ) m.c.m=3.5(x+2 ) m.c.m=15(x+2 )
  9. 10,515b 10=2.5 515b=5(13b ) m.c.m=2.5(13b ) m.c.m=10(13b )
  10. 36 a 2 ,4ax12ay 36 a 2 = 2 2 . 3 2 a 2 4ax12ay=4a(x3y ) = 2 2 a(x3y ) m.c.m= 2 2 . 3 2 a 2 (x3y ) m.c.m=36 a 2 (x3y )
  11. 12x y 2 ,2a x 2 y 3 +5 x 2 y 3 12x y 2 = 2 2 .3x y 2 2a x 2 y 3 +5 x 2 y 3 = x 2 y 3 (2a+5 ) m.c.m= 2 2 .3 x 2 y 3 (2a+5 ) m.c.m=12 x 2 y 3 (2a+5 )
  12. mn, m 2 ,m n 3 m n 2 mn m 2 m n 3 m n 2 =m n 2 (n1 ) m.c.m= m 2 n 2 (n1 )
  13. 2 a 2 ,6ab,3 a 2 6ab 2 a 2 6ab=2.3ab 3 a 2 6ab=3a(a2b ) m.c.m=2.3 a 2 b(a2b ) m.c.m=6 a 2 b(a2b )
  14. x y 2 , x 2 y 3 ,5 x 5 5 x 4 x y 2 x 2 y 3 5 x 5 5 x 4 =5 x 4 (x1 ) m.c.m=5 x 4 y 3 (x1 )
  15. 9 a 2 ,18 b 3 ,27 a 4 b+81 a 3 b 2 9 a 2 = 3 2 a 2 18 b 3 =2. 3 2 b 3 27 a 4 b+81 a 3 b 2 =27 a 3 b(a+3b ) = 3 3 a 3 b(a+3b ) m.c.m=2. 3 3 a 3 b 3 (a+3b ) m.c.m=54 a 3 b 3 (a+3b )
  16. 10,6 x 2 ,9 x 3 y+9x y 3 10=2.5 6 x 2 =2.3 x 2 9 x 3 y+9x y 3 =9xy( x 2 + y 2 ) = 3 2 xy( x 2 + y 2 ) m.c.m=2. 3 2 .5xy( x 2 + y 2 ) m.c.m=90xy( x 2 + y 2 )
  17. 4x, x 3 + x 2 , x 2 yxy 4x= 2 2 x x 3 + x 2 = x 2 (x+1 ) x 2 yxy=xy(x1 ) m.c.m= 2 2 x 2 y(x1 ) (x+1 ) m.c.m=4 x 2 y(x1 ) (x+1 )
  18. 24,6 m 2 +18m,8m24 24= 2 3 .3 6 m 2 +18m=6m(m+3 ) =2.3m(m+3 ) 8m24=8(m3 ) = 2 3 (m3 ) m.c.m= 2 3 .3m(m+3 ) (m3 ) m.c.m=24m(m+3 ) (m3 )
  19. 2 a 2 b 2 ,3ax+3a,6x18 2 a 2 b 2 3ax+3a=3a(x+1 ) 6x18=6(x3 ) =2.3(x3 ) m.c.m=2.3 a 2 b 2 (x+1 ) (x3 ) m.c.m=6 a 2 b 2 (x+1 ) (x3 )
  20. x 2 , x 3 + x 2 2x, x 2 +4x+4 x 2 x 3 + x 2 2x=x( x 2 +x2 ) =x(x+2 ) (x1 ) x 2 +4x+4= (x+2 ) 2 m.c.m= x 2 (x+2 ) 2 (x1 )
  21. 6ab, x 2 4xy+4 y 2 ,9 a 2 x18 a 2 y 6ab=2.3ab x 2 4xy+4 y 2 = (x2y ) 2 9 a 2 x18 a 2 y=9 a 2 (x2y ) = 3 2 a 2 (x2y ) m.c.m=2. 3 2 a 2 (x2y ) 2 m.c.m=18 a 2 (x2y ) 2
  22. 6 x 3 ,3 x 3 3 x 2 18x,9 x 4 36 x 2 6 x 3 =2.3 x 3 3 x 3 3 x 2 18x=3x( x 2 x6 ) =3x(x3 ) (x+2 ) 9 x 4 36 x 2 =9 x 2 ( x 2 4 ) = 3 2 x 2 (x+2 ) (x2 ) m.c.m=2. 3 2 x 2 (x3 ) (x+2 ) (x2 ) m.c.m=18 x 2 (x3 ) (x+2 ) (x2 )
  23. a 2 x 2 ,4 x 3 12 x 2 y+9x y 2 ,2 x 4 3 x 3 y a 2 x 2 4 x 3 12 x 2 y+9x y 2 =x(4 x 2 12xy+9 y 2 ) =x (2x3y ) 2 2 x 4 3 x 3 y= x 3 (2x3y ) m.c.m= a 2 x 3 (2x3y ) 2
  24. 8 x 3 ,12 x 2 y 2 ,9 x 2 45x 8 x 3 = 2 3 x 3 12 x 2 y 2 = 2 2 .3 x 2 y 2 9 x 2 45x=9x(x5 ) = 3 2 x(x5 ) m.c.m= 2 3 . 3 2 x 3 y 2 (x5 ) m.c.m=72 x 3 y 2 (x5 )
  25. a n 3 ,2n, n 2 x 2 + n 2 y 2 ,n x 2 +2nxy+n y 2 a n 3 2n n 2 x 2 + n 2 y 2 = n 2 ( x 2 + y 2 ) n x 2 +2nxy+n y 2 =n( x 2 +2xy+ y 2 ) =n (x+y ) 2 m.c.m=2a n 3 ( x 2 + y 2 ) (x+y ) 2
  26. 8 x 2 , x 3 + x 2 6x,2 x 3 8 x 2 +8x,4 x 3 +24 x 2 +36x 8 x 2 = 2 3 x 2 x 3 + x 2 6x=x( x 2 +x6 ) =x(x+3 ) (x2 ) 2 x 3 8 x 2 +8x=2x( x 2 4x+4 ) =2x (x2 ) 2 4 x 3 +24 x 2 +36x=4x( x 2 +6x+9 ) = 2 2 x (x+3 ) 2 m.c.m= 2 3 x 2 (x2 ) 2 (x+3 ) 2 m.c.m=8 x 2 (x2 ) 2 (x+3 ) 2
  27. 3 x 3 , x 3 +1,2 x 2 2x+2,6 x 3 +6 x 2 3 x 3 x 3 +1=(x+1 ) ( x 2 x+1 ) 2 x 2 2x+2=2( x 2 x+1 ) 6 x 3 +6 x 2 =6 x 2 (x+1 ) =2.3 x 2 (x+1 ) m.c.m=2.3 x 2 (x+1 ) ( x 2 x+1 ) m.c.m=6 x 2 (x+1 ) ( x 2 x+1 )
  28. 4x y 2 ,3 x 3 3 x 2 , a 2 +2ab+ b 2 ,axa+bxb 4x y 2 = 2 2 x y 2 3 x 3 3 x 2 =3 x 2 (x1 ) a 2 +2ab+ b 2 = (a+b ) 2 axa+bxb=a(x1 ) +b(x1 ) =(a+b ) (x1 ) m.c.m= 2 2 .3 x 2 y 2 (a+b ) 2 (x1 ) m.c.m=12 x 2 y 2 (a+b ) 2 (x1 )
  29. 2a,4b,6 a 2 b,12 a 2 24ab+12 b 2 ,5a b 3 5 b 4 2a 4b= 2 2 b 6 a 2 b=2.3 a 2 b 12 a 2 24ab+12 b 2 =12( a 2 2ab+ b 2 ) = 2 2 .3 (ab ) 2 5a b 3 5 b 4 =5 b 3 (ab ) m.c.m= 2 2 .3.5 a 2 b 3 (ab ) 2 m.c.m=60 a 2 b 3 (ab ) 2
  30. 28x, x 2 +2x+1, x 2 +1,7 x 2 +7,14x+14 28x= 2 2 .7x x 2 +2x+1= (x+1 ) 2 x 2 +1 7 x 2 +7=7( x 2 +1 ) 14x+14=14(x+1 ) m.c.m= 2 2 .7x (x+1 ) 2 ( x 2 +1 ) m.c.m=28x (x+1 ) 2 ( x 2 +1 )