It is known that the difference between two natural numbers is 3, and the product of their greatest common divisor and least common multiple is 180 Please write clearly and carefully

It is known that the difference between two natural numbers is 3, and the product of their greatest common divisor and least common multiple is 180 Please write clearly and carefully

Let X and y, because the difference is 3, so the greatest common divisor is 3, the least common multiple is 180 / 3 = 60, and about 60 = 3 * 4 * 5

If the difference between two natural numbers is 3, and the product of their greatest common divisor and least common multiple is 180, what is the larger of the two numbers?

The greatest common divisor refers to the largest common divisor among several integers
Example: in 2,4,6, 2 is the greatest common divisor of 2,4,6
The least common multiple, for two integers, refers to the least common multiple of the two integers
When calculating the least common multiple, it is usually aided by the greatest common factor
The key to this problem lies in the decomposition of 180
180=3×3×2×2×5 =12 x 15
Suppose that the greatest common divisor is 3 and the least common multiple is 60,
The two numbers are 12 and 15, so the larger number is 15
12 = 3 x 4 15 = 3 x 5

It is known that the greatest common divisor of two natural numbers is 15 and the least common multiple is 180. It takes two groups to find out how many of these two numbers are

180/15=12=3*4=1*12
15*3=45 15*4=60
Or 15 * 1 = 15,15 * 12 = 180