6 Compute a gcd150369 bthe prime factorization of 86 clcm86

6. Compute (a) gcd(1503,69) (b)the prime factorization of 86; (c)lcm(86, 18).

Solution

a)gcd(1503,69)

lets divide 1503 by 69 , we get quotient=21 remainder=54

lets divide 69 by 54 we get quotient=1 remainder=15

lets divide 54 by 15 we get quotient=3 remainder=9

lets divide 15 by 9 we get quotient=1 remainder=6

lets divide 9 by 6 we get quotient=1 remainder=3

lets divide 6 by 3 we get quotient=2 remainder=0

so gcd(1503,69)=3

b)prime factoriztion of 86=2*43

c)lcm(86,18)

Multiply each factor the greatest number of times it occurs in any of the numbers. 86 has one 43, and one 2 and 18 has two 3\'s and one 2, so we multiply 3 two times, 2 one time and 43 once. This gives us 774 , the smallest number that can be divided evenly by 86 and 18.

lcm(86,18)=774