Question 3. find the following gcd and lcm: (3.a) gcd(343,550), lcm(343,550). (3.b) gcd(89, 110), lcm(89, 110). (3.c) gcd(870, 222), lcm(870, 222).

GCD(343,550) = 1

LCM(343,550) = 188650

GCD(89,110) = 1

LCM(89,110)  = 9790

GCD(870,222)  = 6

LCM(870,222) = 32190

Step-by-step explanation:

a) GCD(343,550)

343 - 550 | 1

...

There are no values for which both 343 and 550 are divisible by, so GCD(343,550)=1.

LCM(343,550)

343 - 550 | 2

343 - 275 | 5

343 - 55   | 5

343 - 11     | 7

49- 11        | 7

7 - 11        | 7

1 - 11          | 11

1 - 1      

So LCM(343,550) = 2*5*5*7*7*7*11 = 188650

b) GCD(89,110)

Again, as in a), there are no values for which 89 and 110 are divisible by. So GCD(89,110) = 1.

LCM(89,110)

89 - 110 | 2

89 - 55 | 5

89 - 11   | 11

89 - 1    | 89

1 - 1

So LCM(89,110) = 2*5*11*89 = 9790

c) GCD(870,222)

870 - 222 | 2

435 - 111    | 3

145 - 37    

There are no numbers for which 145 and 37 are both divisible by, so the algorithm ends there, and GCD(870,222) = 2*3 = 6

LCM(870,222)

870 - 222 | 2

435 - 111    | 3

145 -  37    | 5

29 - 37      | 29

1 - 37         | 37

1 - 1

So LCM(870,222) = 2*3*5*29*37 = 32190

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction