Question

30, 72 an x are three positive integers. Such that the product of any two of them is
divisible by the third, then the least value of x is​

Answer 1

Answer:

5 ,2, ,4,6,9,10 can be the answer

Step-by-step explanation:

30*72=2160

Answer 2

Answer:

Wrong. The answer must be 60.

Step-by-step explanation:

30, 72, and XThere must exist positive integers A, B, and C such that 30·72 = XA

30X = 72B

72X = 30C

Simplifying:2160 = XA

5 = 12B

12X = 5C

Solving each for X:X = 2160 /AX = 12 B/ 5X = 5 C /12

Set the last two right sides equal, since both are equal to X12 *B/ 5 = 5 * C / 12144B = 25CThe smallest B and C can be are B = 25 and C = 144

Substituting inX = 12B/ 5 = 12*25/ 5 = 60 X = 5C / 12 = 5 * 144/ 12 = 60

That works because30, 72, and 6030*72 = 2160 = 60*3630*60 = 1800 = 73*2560*72 = 4320 = 30*144

So the answer is X = 60