GCD and LCM
donald trump
27/03/2017 at 16:42
Đào Trọng Nghĩa 27/03/2017 at 19:24
Mình chả biết

this question very easy

donald trump
27/03/2017 at 16:39donald trump
27/03/2017 at 16:36
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}

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}
donald trump
27/03/2017 at 16:31

Đào Trọng Nghĩa 27/03/2017 at 19:28
Mình chịu lớp mấy zậy
donald trump
27/03/2017 at 15:25
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 : 20^{2} = 84
Answer : 20 cm ; 84 squares
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Barack Obama 06/04/2017 at 20:08
Hello,my friend

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

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.
donald trump
27/03/2017 at 14:02
1998 = 2 x 3^{3} 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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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

»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
donald trump
27/03/2017 at 14:03
3432 = 2^{3} x 3 x 11 x 13
5460 = 2^{2} x 3 x 5 x 7 x 13
=> GCD (3432 ; 5460) = 2^{2} 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 12:41We 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
donald trump
27/03/2017 at 14:05
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

donald trump
27/03/2017 at 14:08
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 : 15^{2} = 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
donald trump
27/03/2017 at 14:06
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

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
donald trump
27/03/2017 at 14:35
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

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