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GDC and LCM

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Thao Dola
20/03/2017 at 14:13
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3
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The lowest common multiple of a and b is 50. List all possible values of a and b.

GDC and LCM

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    In the name of love 20/03/2017 at 14:45

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

    Good! ^^

  • ...
    Nguyễn Ngọc Mai 21/03/2017 at 10:30

    \(a,b\in\) { 1 ; - 1 ; 2 ; -2 ; -5 ; 5 ; 10 ; -10 ; -25 ; 25 ; 50 ; -50 } 

    1 l i k e ! Hihi

    undefinedundefinedundefinedundefined

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    Love people Name Jiang 20/03/2017 at 17:12

    BCNN (a,b) = 50 => a,b = 25;50 . 10;50 . 1;50 . 2;50 . 5;50 

    Good  


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Thao Dola
20/03/2017 at 14:12
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2
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The greatest common dividor of m and n is 15.Given 3m+2n = 225, find mn.

GDC and LCM

  • ...
    FA KAKALOTS 09/02/2018 at 22:03

    Because the greatest common dividor of m and n is 15, we put:

     {m=15kn=15h

    (GCD(k;h)=1)

    ⇒3m+2n=45k+30h=225

    ⇒15(3k+2h)=225⇒3k+2h=15

    + If h = 0 then k = 5; and that result doesn't satisfy GCD(k;h) = 1.

    So h > 0; then k is an odd number. 

    3k<15⇒k<5⇒k∈{1;3}

    If k = 1 then h = 6⇒

     m = 15 ; n = 90 ⇒mn=15.90=1350

    If k = 3 then h = 3; that result doesn't satisfy GCD(k;h)=1.

    Therefore, the answer is 1350.

  • ...
    ♫ ♪ ♥► EDM Troop ◄♥ ♪ ♫ 22/03/2017 at 20:41

    Because the greatest common dividor of m and n is 15, we put:

     \(\left\{{}\begin{matrix}m=15k\\n=15h\end{matrix}\right.\)\(\left(GCD\left(k;h\right)=1\right)\)

    \(\Rightarrow3m+2n=45k+30h=225\)

    \(\Rightarrow15\left(3k+2h\right)=225\Rightarrow3k+2h=15\)

    + If h = 0 then k = 5; and that result doesn't satisfy GCD(k;h) = 1.

    So h > 0; then k is an odd number. 

    \(3k< 15\Rightarrow k< 5\Rightarrow k\in\left\{1;3\right\}\)

    If k = 1 then h = 6\(\Rightarrow\) m = 15 ; n = 90 \(\Rightarrow mn=15.90=1350\)

    If k = 3 then h = 3; that result doesn't satisfy GCD(k;h)=1.

    Therefore, the answer is 1350.


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Thao Dola
20/03/2017 at 14:11
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5
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A cardboard \(140cm\times240cm\) is cut into many congruent squares. What is the largest possible square size? How many squares can be cut from the cardboard without wastage?

GDC and LCM

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    »ﻲ†hïếu๖ۣۜGïลﻲ« 25/03/2017 at 19:06

    We have : ƯCLN(140;240) = 20

    Dress the largest square can be 20 cm x 20 cm

  • ...
    →இے๖ۣۜQuỳnh 22/03/2017 at 20:20

    We have : ƯCLN(140;240) = 20

    Dress the largest square can be 20 cm x 20 cm

  • ...
    Love people Name Jiang 20/03/2017 at 17:23

    We have : ƯCLN(140;240) = 20

    Dress the largest square can be 20 cm x 20 cm


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Thao Dola
20/03/2017 at 14:08
Answers
4
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The product of a grandfather's age and hos grandchild's age is 1339 next year. How old are they now?

GDC and LCM

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    FA KAKALOTS 09/02/2018 at 22:04

    1339 = 103 x 13 = 1 x 1339.

    No one can be 1339 years old, so the grandfather will be 103 years old and his grandchild will be 13 years old next year.

    Thus, the grandfather is 102 years old, and his grandchild is 12 years old now.

  • ...
    Lê Nho Khoa 23/03/2017 at 21:04

    1339 = 103 x 13 = 1 x 1339.

    No one can be 1339 years old, so the grandfather will be 103 years old and his grandchild will be 13 years old next year.

    Thus, the grandfather is 102 years old, and his grandchild is 12 years old now.

  • ...
    hghfghfgh 26/03/2017 at 20:12

    1339 = 103 x 13 = 1 x 1339.

    No one can be 1339 years old, so the grandfather will be 103 years old and his grandchild will be 13 years old next year.

    Thus, the grandfather is 102 years old, and his grandchild is 12 years old now.


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Thao Dola
20/03/2017 at 14:06
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3
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The remain der 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?

GDC and LCM

  • ...
    FA KAKALOTS 09/02/2018 at 22:04

    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

  • ...
    Lê Nho Khoa 23/03/2017 at 21:05

    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 22/03/2017 at 21:14

    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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Thao Dola
20/03/2017 at 14:03
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2
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Alvin, Ben, Carl and Dan are salesmen for refrigerators. In 2009, Alvin sold 7 times as many refrigerators sold by Ben, 5 times as many sold by Carl and 4 times as many sold by Dan. In all, the 4 salesmen sold 669 refrigerators.What would be the highest possible number of refrigerators Alvin had sold?

GDC and LCM

  • ...
    FA KAKALOTS 09/02/2018 at 22:04

    Let 140a be the number of refrigerators Alvin sold in 2009, where a is a constant value. Thus,

    - Ben sold 140a ÷

     7 = 20a (refrigerators);

    - Carl sold 140a ÷

     5 = 28a (refrigerators);

    - Dan sold 140a ÷

     4 = 35a (refrigerators).

    According to the problem, we have,

    140a + 20a + 28a + 35a = 669

    223a = 669

    a = 3.

    Therefore, Alvin had sold at most 3 ×

     140 = 420 refrigerators.
    Answer : 420

  • ...
    Nguyễn Nhật Minh 29/05/2017 at 20:57

    Let 140a be the number of refrigerators Alvin sold in 2009, where a is a constant value. Thus,

    - Ben sold 140a \(\div\) 7 = 20a (refrigerators);

    - Carl sold 140a \(\div\) 5 = 28a (refrigerators);

    - Dan sold 140a \(\div\) 4 = 35a (refrigerators).

    According to the problem, we have,

    140a + 20a + 28a + 35a = 669

    223a = 669

    a = 3.

    Therefore, Alvin had sold at most 3 \(\times\) 140 = 420 refrigerators.

    Answer. 420 refrigerators


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Thao Dola
20/03/2017 at 14:00
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When the three numbers 995.1233 and 1928 are divided by positive integer m, the remainders are all equal to a positive integer n. Find \(m+n\).

GDC and LCM


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Thao Dola
20/03/2017 at 13:59
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Two types of marking are carried out on a steel rod 1m long. There is a blue marking every 6cm from left to right. There is also a red marking every 5cm from right to left. How many segment are of 1cm.

GDC and LCM


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Thao Dola
20/03/2017 at 13:56
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Three types of beverage were served at a wedding dinner. 2 persons shared a can of beer. 3 persons shared a jar of fruit punch. 4 persons shared a bootle of wine. 78 cans of beverage were served altogether. How many guests were at the dinner?

GDC and LCM


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Thao Dola
20/03/2017 at 13:54
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3
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The remainder is 1 when a certain number is divided by 2. The Remainder is also 1 when the divisors are 3,4,5 and 6 respectively.

What is the smaillest possible of this number?

GDC and LCM

  • ...
    FA KAKALOTS 09/02/2018 at 22:05

    Let n be the smallest value of that number. When n is divided by 2,3,4,5,6,the remainder is always 1,so n - 1 is divisible by 2,3,4,5,6

    => n - 1 = LCM(2,3,4,5,6) = 60 => n = 61

  • ...
    Lê Nho Khoa 23/03/2017 at 21:05

    Let n be the smallest value of that number. When n is divided by 2,3,4,5,6,the remainder is always 1,so n - 1 is divisible by 2,3,4,5,6

    => n - 1 = LCM(2,3,4,5,6) = 60 => n = 61

  • ...
    Phan Thanh Tinh Coordinator 22/03/2017 at 21:18

    Let n be the smallest value of that number. When n is divided by 2,3,4,5,6,the remainder is always 1,so n - 1 is divisible by 2,3,4,5,6

    => n - 1 = LCM(2,3,4,5,6) = 60 => n = 61


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Thao Dola
20/03/2017 at 13:52
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2
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Find The greatest common divsor and lowes common multiple of  (882,1134).

GDC and LCM

  • ...
    FA KAKALOTS 09/02/2018 at 22:05

    We have : 882 = 2 x 32 x 72 ; 1134 = 2 x 34 x 7.So :

    GCD(882 ; 1134) = 2 x 32 x 7 = 126

    LCM(882 ; 1134) = 2 x 34 x 72 = 7938

  • ...
    Phan Thanh Tinh Coordinator 22/03/2017 at 21:20

    We have : 882 = 2 x 32 x 72 ; 1134 = 2 x 34 x 7.So :

    GCD(882 ; 1134) = 2 x 32 x 7 = 126

    LCM(882 ; 1134) = 2 x 34 x 72 = 7938


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