 5. Find the least common multiple (lcm) of the pairs of integers gi... 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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