If the greatest common factor of two numbers is 16 and the least common multiple is 480, and the difference between the two numbers is 16, what are the two numbers?

If the greatest common factor of two numbers is 16 and the least common multiple is 480, and the difference between the two numbers is 16, what are the two numbers?


Because 480 = 16 × 30, it can be seen that the product of quotient obtained by two numbers △ 16 is equal to 30; and 30 = 2 × 15 = 3 × 10 = 5 × 6, so these two numbers are: 5 × 16 = 80 and 6 × 16 = 96; answer: these two numbers are 80 and 96



The greatest common divisor of two positive integers is 6, and the least common multiple is 90. How many pairs of large numbers composed of two positive integers meet the condition?


Suppose these two positive integers are a and B, and a > B
Therefore, we can get that a / 6 and B / 6 are positive integers, and their greatest common divisor is 6 / 6 = 1, and their least common divisor is 90 / 6 = 15
From this, we can get a / 6 = 15, B / 6 = 1, or a / 6 = 5, B / 6 = 3
So, a = 90, B = 6; or, a = 30, B = 18. There are two pairs



If the greatest common divisor of the sum of two numbers is 16 and the least common multiple is 480, and the sum of the two numbers is 16, what are the two numbers


80 and 96



If the greatest common factor of two numbers is 16 and the least common multiple is 480, and the difference between the two numbers is 16, what are the two numbers?


Because 480 = 16 × 30, it can be seen that the product of quotient obtained by two numbers △ 16 is equal to 30; and 30 = 2 × 15 = 3 × 10 = 5 × 6, so these two numbers are: 5 × 16 = 80 and 6 × 16 = 96; answer: these two numbers are 80 and 96