Solution: this problem can be summarized as "a number divided by 3 1, divided by 5 by 2, and divided by 7 by 3." What is the smallest number? " Let's talk about the remainder first: because the remainder 1 is divided by 3, this number is 3n+ 1(n is a positive integer). In order to make the number 3n+ 1 satisfy the condition that the remainder 2 is divided by 5, we can try to substitute n= 1, 2, 3 ... and find that when n=2, 3×2+ 1=7 satisfies the condition. Since 15 can be divisible by 3 and 5, the number 15m+7 (m is a positive integer) can also satisfy the two conditions that 1 is divisible by 3 and 2 is divisible by 5. Choose an appropriate m in 15m+7 and divide it by 7 to get the remainder 3. The method of trial generation is also adopted, and the results of trial generation show that the conditions are met when m=3.

So the answer is 15×3+7= 52, which means there are at least 52 peaches in this basket. Is there a law to solve this problem of dividing by 3, 5 and 7 to get different remainders respectively? Yes China has a famous remainder theorem, and four poems can be vividly remembered. Three people travel seventy miles, five trees and twenty-one clubs, seven children and a half months of reunion, and you will know when you throw five. These four poems are called "Sun Zi Dian Bing" and "Chinese remainder theorem" in foreign countries. The meaning of this poem is: 70 times the remainder obtained by dividing by 3, 2 1 times the remainder obtained by dividing by 5, 15 times the remainder obtained by dividing by 7, and then add these three products, and you can add or subtract the integer multiple of 105 to get the desired number. Now let's go back to this problem and solve it in the above way. Since 3 divides the remainder 1, 5 divides the remainder 2, and 7 divides the remainder 3,70×1+21× 2+15× 3 = 70+42+45 =157.

Because the minimum value is required, 157- 105 = 52.