any 2 positive integers in the ratio 7:12 to the product of hcf is 4 and lcm is 4xy. find the two numbers x and y
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Answer:
16 and 12
Step-by-step explanation:
As HCF of the two numbers is 4, it is safe to assume that the two numbers are 4x and 4y where x and y do not share any common factors
Thus their sum is 4(x+y) and their LCM is 4xy
So 4(x+y) : 4xy = 7 : 12
x+y : xy = 7 : 12
It is easy to observe that x = 4 and y = 3 are valid values, which gives the two natural numbers as 4x4 and 4x3, ie 16 and 12
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