Question

5. Find the least common multiple (lcm) of the pairs of integers given in exercises 4. These were:
a). a=1,575 and b=231
b). a = -3719, b = 8416
c). a = 28,844, b = -15,712

6. Find the prime numbers less than or equal to the following natural numbers.
a) less than 200
b) less than 500

7. Find a (mod n) in each of the following cases.
a) a = 43,197, n = 39
b) a = -125,617, n = 315

8. Find a solution in each of the following congruencies
a) x = 7 (mod 9)
b) x = 4 (mod 12)
c) x = 16 (mod 21)

Solution Preview

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5.
a.
a=1,575 and b=231
We try to decompose each of the two numbers.
1,575=5* 315=5*5*63=5*5*3*21=5*5*3*3*7=3²*5²*7
231=3*77=3*7*11
This case LCM=3²*5²*7*11=17,325...

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