Question

The sum of two numbers is 31 and the product is 238 then what will be the lcm

Answer 1

Step-by-step explanation:

Let the required numbers be x and y.

Hence, according to the given information:

x + y = 31. ...... (1)

xy = 238 .........(2)

Since

$( {x - y})^{2} = ( {x + y})^{2} - 4xy \: ....(3) \\ from \: equations \: (1) \: (2) \: and \: (3) \\ ( {x - y})^{2} = ({31})^{2} - 4 \times 238 \\ ( {x - y})^{2} = 961 - 952 \\ ( {x - y})^{2} = 9 \\ {x - y} = 3 \: \: .....(4) \\ adding \: (1) \: and \: (4) \: we \: find \\ 2x = 34 \\ x = 17 \\ y = 14 \\ lcm \: of \: 17 \: and \: 14 \: = 17 \times 14 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 238$