Question 5\ Let

m=[a,b]

be the least common multiple of positive integers

a

and

b

, and

c

be another (larger) common multiple of

a

and

b

. Prove that

m

divides

c

.\ (Hint: Use the division theorem on

m

and

c

, and show that the remainder

r

is divisible by

a

and

b

. Then argue why this implies that

r=0

).\ Solution:

Let m=[a,b] be the least common multiple of positive integers a and b, and c be another (larger) common multiple of a and b. Prove that m divides c. (Hint: Use the division theorem on m and c, and show that the remainder r is divisible by a and b. Then argue why this implies that r=0 )