The greatest common divisor of the two natural numbers a and B is 6, and the least common multiple is 90. How many pairs of numbers meet this condition? Please be clear,

The greatest common divisor of the two natural numbers a and B is 6, and the least common multiple is 90. How many pairs of numbers meet this condition? Please be clear,


According to the least common multiple, we can get 1 * 90 = 90, 2 * 45 = 90, 3 * 30 = 90, 5 * 18 = 90, 6 * 15 = 90, 9 * 10 = 90
Among the factors of these formulas, 1,2,3,4,5,9,10,15,45 are not multiples of six, and 6,18,30,90 are multiples of six
So, there are four pairs, 6 and 18, 6 and 30, 6 and 90, 18 and 30



Two natural numbers are two digits. Their greatest common divisor is 6 and their least common multiple is 90. What is the sum of these two natural numbers
Write down the process


90 △ 6 = 15 15 = 3 × 5 = 1 × 15 (3 + 5) × 6 = 48 (1 + 15) × 6 = 96 the sum of these two numbers is 48 or 96 respectively



The difference between two natural numbers is 90, and the sum of the greatest common divisor and the least common multiple is 240


Let the greatest common divisor of two numbers be m, then the first number is km, and the second number is LM, K, l coprime. Then the least common multiple is KLM, so we can know from the question: km-lm = 90, that is, (K-L) M = 90, 1 Formula M + KLM = 240, that is, (1 + KL) M = 240 = 8 * 2 * 15, 2 formula (1 + KL) / (K-L) = 8 / 3



If the difference between two natural numbers is 5 and the difference between their least common multiple and greatest common divisor is 203, then the sum of the two numbers is______ .


① If two numbers have a common divisor 5, obviously the least common multiple is also a multiple of 5, the difference between the least common multiple and the greatest common divisor must be a multiple of 5, obviously 203 is not a multiple of 5, so the first case does not meet, then the two numbers are coprime; ② when the two numbers are coprime, the maximum common divisor of the two coprime numbers is 1, so the two