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GCD and LCM

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donald trump
27/03/2017 at 16:42
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There are three kinds of marking on a rope. The red markings divide the rope evenly into 10 parts. The blue markings divide the rope equally into 12 parts. The yellow markings divide the rope evently into 15 parts. How many segments does the rope have now?

GCD and LCM

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    Đào Trọng Nghĩa 27/03/2017 at 19:24

    Mình chả biết

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    falcon handsome moderators 27/03/2017 at 17:20

    this question very easy

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    Bonobos 29/03/2017 at 14:15

    There are 32 segments . 

    please, me off.


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donald trump
27/03/2017 at 16:39
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2000 soldiers line up in a row. In the first round . They report "1,2", "1,2" and so on. Those who report "2" remain in the line. From the 2nd round onwards, they report in this manner: 1,2,3,1,2,3,... In each round, those who report "2" remain in the line, until only one soldier is left. What is the original number of this soldier

GCD and LCM


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donald trump
27/03/2017 at 16:36
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The lowest common multiple of a and b is 50. List all possible values of a and b

GCD and LCM

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    FA KAKALOTS 09/02/2018 at 22:00

    Because the lowest common multiple of a and b is 50 . So all possible values of a and b is :

    (a;b) = {1 ; 2 ; 5 ; 10 ; 25 ; 50}

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    Indratreinpro 02/04/2017 at 22:07

    Because the lowest common multiple of a and b is 50 . So all possible values of a and b is :

    (a;b) = {1 ; 2 ; 5 ; 10 ; 25 ; 50}

  • ...
    Number One 02/04/2017 at 06:26

    Because the lowest common multiple of a and b is 50 . So all possible values of a and b is :

    (a;b) = {1 ; 2 ; 5 ; 10 ; 25 ; 50}


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donald trump
27/03/2017 at 16:31
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The greatest common divisor ò m and n is 15 . Given 3m + 2n = 225,

find mn.

GCD and LCM

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    Phan Văn Hiếu 28/03/2017 at 21:26

    m=45;n=45        

             

  • ...
    Đào Trọng Nghĩa 27/03/2017 at 19:28

    Mình chịu lớp mấy zậy


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donald trump
27/03/2017 at 15:25
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A cardboard 140cm x 240cm is cut into many congruent squares. What is the largest possible square size ? How many suqares can be cut from the cardboard without wastage?

GCD and LCM

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    Phan Thanh Tinh Coordinator 27/03/2017 at 22:29

    Let a (cm) be the largest possible square size

    => a = GCD (140 ; 240) = 20 

    So the largest size of the square's edge is 20 cm.Then the smallest number of squares can be cut from the cardboard is :

    140 x 240 : 202 = 84

    Answer : 20 cm ; 84 squares

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    Barack Obama 06/04/2017 at 20:08

    Hello,my friend

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    Nếu bây giờ ngỏ ý . Liệu có còn kịp không 28/03/2017 at 12:36

    Let a (cm) be the largest possible square size

    => a = GCD (140 ; 240) = 20 

    So the largest size of the square's edge is 20 cm.Then the smallest number of squares can be cut from the cardboard is :

    140 x 240 : 202 = 84

    Answer : 20 cm ; 84 squares


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donald trump
27/03/2017 at 15:13
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The product of a grandfather's age and his grandchild's age is 1330 next year. How old are they now?

GCD and LCM

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    Phan Thanh Tinh Coordinator 27/03/2017 at 22:44

    1330 = 2 x 5 x 7 x 19 = 2 x 7 x 5 x 19 = 14 x 95

    So the grandpa's age and his grandchild's age next year should be 95 and 14 respectively.Then now,the grandpa is 94 and his grandchild is 13

    donald trump selected this answer.

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donald trump
27/03/2017 at 14:02
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The number 1998 has x factors . Find x

GCD and LCM

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    Phan Thanh Tinh Coordinator 27/03/2017 at 22:39

    1998 = 2 x 33 x 37,then 1998 has : (1 + 1)(3 + 1)(1 + 1) = 16 (factors)

    So x = 16

    P/S : 16 is the number of positive factors of 1998,so 1998 has 32 integer factors

    Selected by MathYouLike
  • ...
    FA KAKALOTS 09/02/2018 at 22:01

    1998 = 2 x 33 x 37,then 1998 has : (1 + 1)(3 + 1)(1 + 1) = 16 (factors)

    So x = 16

    P/S : 16 is the number of positive factors of 1998,so 1998 has 32 integer factors

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    »ﻲ2004#ﻲ« 29/03/2017 at 06:11

    1998 = 2 x 33 x 37,then 1998 has : (1 + 1)(3 + 1)(1 + 1) = 16 (factors)

    So x = 16

    P/S : 16 is the number of positive factors of 1998,so 1998 has 32 integer factors


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donald trump
27/03/2017 at 14:03
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The greatest common divisor of (3432, 5460) is ?

GCD and LCM

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    Phan Thanh Tinh Coordinator 27/03/2017 at 22:35

    3432 = 23 x 3 x 11 x 13

    5460 = 22 x 3 x 5 x 7 x 13

    => GCD (3432 ; 5460) = 22 x 3 x 13 = 156

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  • ...
    »ﻲ2004#ﻲ« 29/03/2017 at 06:12

    3432 = 23 x 3 x 11 x 13

    5460 = 22 x 3 x 5 x 7 x 13

    => GCD (3432 ; 5460) = 22 x 3 x 13 = 156

     
  • ...
    Nễu Lả Ánh 28/03/2017 at 12:41
    We have 3432 = 23 x 3 x 11 x 13

    5460 = 22 x 3 x 5 x 7 x 13

    => GCD (3432 ; 5460) = 22 x 3 x 13 = 156


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donald trump
27/03/2017 at 14:05
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a * b * c * d  * e = 2000, where each of a,b,c,d and e is greater than 1. The smallest possible value of a + b + c +d + e is ? 

GCD and LCM

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    FA KAKALOTS 09/02/2018 at 22:01

    2000=2^4 * 5^3 = 2*2*2*2*125 = 5*5*5*2*8

    => min (a+b+c+d)=5+5+5+2+8=25

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    Nhat Lee 16/04/2017 at 17:28

    2000=2^4 * 5^3 = 2*2*2*2*125 = 5*5*5*2*8

    => min (a+b+c+d)=5+5+5+2+8=25


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donald trump
27/03/2017 at 14:08
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Tiles of 30 cm x 45 cm are used to from a square flooring . The minimum number of tiles used is y pieces Find y?

GCD and LCM

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    Phan Thanh Tinh Coordinator 27/03/2017 at 22:33

    To use the smallest number of tiles,the size of each tile must be the largest.Let x (cm) be that size,so we have x = GCD(30 ; 45) = 15

    => y = 30 x 45 : 152 = 6

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  • ...
    FA KAKALOTS 09/02/2018 at 22:02

    To use the smallest number of tiles,the size of each tile must be the largest.Let x (cm) be that size,so we have x = GCD(30 ; 45) = 15

    => y = 30 x 45 : 152 = 6

  • ...
    Number One 02/04/2017 at 06:28

    To use the smallest number of tiles,the size of each tile must be the largest.Let x (cm) be that size,so we have x = GCD(30 ; 45) = 15

    => y = 30 x 45 : 152 = 6


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donald trump
27/03/2017 at 14:06
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The greatest common divisor of a and b is 8 . Their lowest common multiple is 96

a+b = ? 

GCD and LCM

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    FA KAKALOTS 09/02/2018 at 22:02

    Let [a,b] be the LCM of a and b, and (a,b) be the GCD of a and b.

    Since (a,b) = 8, [a,b] = 96, then a ×

     b = [a,b] × (a,b) = 96 ×

     8 = 768.

    As (a,b) = 8, let a = 8m, b = 8n, in which (m,n) = 1.

    => a ×

     b = 8m × 8n = 768. Thus, m × n = 768 ÷ (8 ×

     8) = 12.

    (m,n) = 1, so all the pairs (m;n) which have GCD = 1 and m ×

     n = 12 are:

    (1;12),(3;4),(4;3),(12;1).

    => (a;b) = (8;96),(24;32),(32;24),(96;8).

    Therefore, there are 2 possible values of a + b: 8+ 96 = 104, 24 + 32 = 56.

    Answer. 104 and 56

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    Nguyễn Nhật Minh 29/05/2017 at 12:30

    Let [a,b] be the LCM of a and b, and (a,b) be the GCD of a and b.

    Since (a,b) = 8, [a,b] = 96, then a \(\times\) b = [a,b] \(\times\) (a,b) = 96 \(\times\) 8 = 768.

    As (a,b) = 8, let a = 8m, b = 8n, in which (m,n) = 1.

    => a \(\times\) b = 8m \(\times\) 8n = 768. Thus, m \(\times\) n = 768 \(\div\) (8 \(\times\) 8) = 12.

    (m,n) = 1, so all the pairs (m;n) which have GCD = 1 and m \(\times\) n = 12 are:

    (1;12),(3;4),(4;3),(12;1).

    => (a;b) = (8;96),(24;32),(32;24),(96;8).

    Therefore, there are 2 possible values of a + b: 8+ 96 = 104, 24 + 32 = 56.

    Answer. 104 and 56


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donald trump
27/03/2017 at 14:35
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The remainder is 2 when n is divided by 3. The remainder is 3, 4 and 5 when the divisors are 4, 5 and 6 respectively. What is the smallest possible of n?

GCD and LCM

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    FA KAKALOTS 09/02/2018 at 22:03

    We have : 3 - 2 = 4 - 3 = 5 - 4 = 6 - 5 = 1

    So n + 1 is divisible by 3,4,5,6 but we need to find the smallest value of n.

    => n + 1 = LCM(3,4,5,6) = 60 => n = 59

  • ...
    Phan Thanh Tinh Coordinator 24/04/2017 at 16:32

    We have : 3 - 2 = 4 - 3 = 5 - 4 = 6 - 5 = 1

    So n + 1 is divisible by 3,4,5,6 but we need to find the smallest value of n.

    => n + 1 = LCM(3,4,5,6) = 60 => n = 59


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