Question

the LCM of two consecutive odd number is 483 them which even number is in between that two consecutive odd numbers

Answer 1

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$let \: the \: two \: consecutive \: odd \: numbers \: be \: (2x + 1) \: and \: (2x + 3) \\ if \: one \: of \: the \: number \: is \: prime \: number \: then \: their \: lcm \: is \: their \: product \: \\ (2x + 1)(2x + 3) = 483 \\ 4 {x}^{2} + 6x + 2x + 3 = 483 \\ 4( {x}^{2} + 2x) = 483 - 3 \\ {x}^{2} + 2x = 480 \div 4 \\ {x}^{2} + 2x - 120 = 0 \\ {x}^{2} + 12x - 10 - 120 = 0 \\ x(x + 12) - 10(x + 12) = 0 \\( x + 12)(x - 10) = 0 \\ x + 12 = 0 \: and \: x - 10 = 0 \\ x = - 12 \: and \: x = 10 \\ negative \: numbers \: are \: neglated \: \\ 2(10) + 1 = 21 \\ 2(10) + 3 = 23 \\ the \: even \: number \: between \: them \: is \: 22$

Answer 2

Step-by-step explanation:

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