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 16:39

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}


Đào Trọng Nghĩa 27/03/2017 at 19:28
Mình chịu lớp mấy zậy

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

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.

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

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

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


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

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

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