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