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:
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