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Mathematical search for regular triangle
There are two possibilities (three in each rotation and six in * * *).

40

15,30

20,60, 10

Or,

15

20,40

60, 10,30

Method 1:

10,20,40 is a multiple, and15,30,60 is also a multiple. Should be placed in the corresponding position, that is, in the middle or corner.

Method 2:

First, decompose the prime factor.

10=2*5

15=3*5

20=2*2*5

30=2*3*5

40=2*2*2*5

60=2*2*3*5

Both of them contain prime factors 5, which can ensure that the number of factors 5 on each side is the same, both of which are 3; The prime number factors are 15, 30 and 60, and their distribution positions are either in the middle of three sides or on three vertices to ensure the same number of factors 3 on each side; Fill with the number of 2, so that the product of 3 numbers on each side of the triangle is equal: Figure 1 Yes 1200, Figure 2 is 1800.

(The above is for reference only)