The quotient of the least common multiple of a and B divided by their greatest common divisor is 12, and the difference between a and B is 18

The quotient of the least common multiple of a and B divided by their greatest common divisor is 12, and the difference between a and B is 18

Let a be ax, B be ay and x > y, x, y be coprime. So the least common multiple of a and B is ax. There are xy = 12, ax ay = a (X-Y) = 18. If a and B are all positive integers, then x and y are also positive integers. There are also 12 = 4 * 3 = 6 * 2  x = 4, y = 3 or x = 6, y = 2 (6 and 2)

If the difference between the two numbers is 18, find the two numbers!

Let these two numbers be a and B, and let the least common multiple be m and the greatest common factor be m
It is known that M = 12M, so mm = 12m ^ 2
That is ab = 12m ^ 2
So a / m * B / M = 12
1) If a / M = 1, B / M = 12, then a = m, B = 12M, B-A = 11m = 18, there is no solution
2) If a / M = 2, B / M = 6, then a = 2m, B = 6m, B-A = 4m = 18, there is no solution
3) A / M = 3, B / M = 4, then a = 3M, B = 4m, B-A = M = 18, so a = 54, B = 72
These two numbers are 54 and 72

The quotient of the least common multiple of a and B divided by their greatest common factor is 12. If the difference between a and B is 18, then a is 12______ The number B is______ ．

The least common multiple of a and B numbers is the greatest common factor of 12 times, where 12 = 3 × 4, or 2 × 6, but there are divisors between 2 and 6. Decompose 12 into the product of 3 and 4, the greatest common factor × (4-3) = 18, the greatest common factor = 18, and 3 × 18 = 54, 4 × 18 = 72. The two numbers of a and B are 54 and 72 respectively