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______ .

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



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



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 their 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 conform, then the two numbers are mutually prime; ② When the two numbers are coprime, the greatest common divisor of the two numbers of the coprime is 1, so the least common multiple of the two numbers is 203 + 1 = 204; and because the two numbers are coprime, the least common multiple of the two numbers is their product, so the two numbers are multiplied by 204, and 204 is decomposed into the prime factor: 204 = 2 × 2 × 3 × 17, so the two numbers are 12 and 17 respectively, and the two numbers are 12 and 17 The sum is 12 + 17 = 29