GDC and LCM


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 !

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

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.

»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
The product of a grandfather's age and hos grandchild's age is 1339 next year. How old are they now?

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.

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

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

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

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

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

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

We have : 882 = 2 x 3^{2} x 7^{2} ; 1134 = 2 x 3^{4} x 7.So :
GCD(882 ; 1134) = 2 x 3^{2} x 7 = 126
LCM(882 ; 1134) = 2 x 3^{4} x 7^{2} = 7938