Question

for two positive integers a and b, we know g c d (a comma b )equals 15 comma space l c m (a comma b )equals 90, what is a b?

Answer 1

Two positive integers have gcd (a, b) = 15 and lcm (a, b) = 90. Those two numbers are 15 and 90 or 30 and 45.

Suppose we have 2 positive integers, a and b, then:

gcd (a, b) = the greatest common divisor = common prime factors of a and b

lcm (a, b) = the least common multiple = multiplication of the greatest common prime factors of a and b

In the given problem:

gcd (a, b) = 15

prime factorization of 15:

15 = 3 x 5

Hence,

a = 3 x 5 x ....

b = 3 x 5 x ....

lcm (a, b) = 90

prime factorization of 90:

90 = 3 x 5 x 2 x 3

Therefore the possible pairs of a and b are:

Combination 1:

a = 3 x 5 = 15

b = 3 x 5 x 2 x 3 = 90

Combination 2:

a = 3 x 5 x 2 = 30

b = 3 x 5 x 3 = 35

We can conclude the two integers are 15 and 90 or 30 and 45.

Learn more about gcd here:

brainly.com/question/16969353

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