The greatest common factor of two natural numbers is 6, and the least common multiple is 240. There are several groups of two natural numbers that meet the conditions Why do you try to translate the reason into formula with additional words? Thank you

The greatest common factor of two natural numbers is 6, and the least common multiple is 240. There are several groups of two natural numbers that meet the conditions Why do you try to translate the reason into formula with additional words? Thank you

Carry out factor decomposition
240=1*1*2*2*2*2*3*5
And because the greatest common factor of two natural numbers is 6, so
Two natural numbers must be multiples of 6,
Let 2 natural numbers be 6m and 6N respectively
And m and N are prime numbers
M and N must be the product of {1,1,2,2,2,5} elements
When m = 1, n = 1 * 2 * 2 * 5 = 40 is consistent with (m, n coprime) (6240)
When m = 2, n = 1 * 1 * 2 * 2 * 5 = 20 does not conform (m, n are not coprime)
When m = 5, n = 1 * 1 * 2 * 2 * 2 = 8 is consistent with (m, n coprime) (30,48)
So there are only two groups

The least common multiple of two continuous natural numbers is 240. These two numbers are () and (), and their greatest common factor is ()

The least common multiple of two continuous natural numbers is 240. These two numbers are (15) and (16) respectively, and their greatest common factor is (1)

Given a △ B = 8, the greatest common factor of a and B is______ The least common multiple is______ ．

According to a △ B = 8, we can get that a is 8 times of B, so the greatest common factor of a and B is B, and the least common multiple is a