Analysis: According to the meaning of the question, it is not difficult to see that the number of children in this large class is the greatest common divisor of 1 15-7 = 108, 148-4= 144, 74-2=72. So this big class has at most 36 children.
Grandpa said to Xiaoming, "I am seven times your age now, six times your age in a few years, five times, four times, three times and two times your age in a few years." Do you know the age of Grandpa and Xiaoming now?
Analysis: The ages of Grandpa and Xiaoming are changing with the passage of time, but their age difference remains the same. Grandpa's age is now seven times that of Xiaoming, indicating that their age difference is a multiple of 6; Similarly, their age difference is 5, 4, 3, 2, 1 times, and the number of tax collectors is set. It can be inferred that their age difference is a common multiple of 6, 5, 4, 3 and 2. [6,5,4,3,2] = 60, and the age difference between Grandpa and Xiaoming is an integer multiple of 60. Considering the actual situation of age, the age difference between grandpa and Xiaoming should be 60 years old. So now Xiaoming's age is 60 ÷ (7- 1) = 10 (years old).
Grandpa's age = 10×7=70 (years).
3. Given that the greatest common divisor of two natural numbers is 4 and the least common multiple is 120, find these two numbers.
Analysis: These two numbers are 4 and 120, or 8 and 60, or 12 and 40, or 20 and 24.
The sum of two natural numbers is 50, and their greatest common divisor is 5. Try to find out the difference between these two numbers.
Analysis: Two numbers can be: 7,49 or 2 1, 35.
; Then the difference is 42, 14.