Question

the product of two consecutive odd numbers is 575 ...Find their lcm ...asap

Answer 1

let the two odd numbers be 2x+1 and 2x+3
given product of two consecutive odd numbers is 575
that is (2x+1)(2x+3)=575
=>4x²+8x+3=575
=>4x²+8x=572
=>4x(x+2)=572
=>x(x+2)=143
=>x(x+2)=(11)(13)
hence X =11
there fore two consecutive odd numbers are 2x+1 and 2x+3=>23 and 25
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Answer 2

Product of two consecutive odd number is 575. Then the LCM is 575

Solution:

Let the two consecutive odd numbers be m and m + 2

Product of two consecutive odd number is 575

Therefore,

$m(m+2) = 575\\\\m^2 + 2m - 575 = 0\\\\\mathrm{Break\:the\:expression\:into\:groups} \\\\\left(m^2-23m\right)+\left(25m-575\right) = 0 \\\\\mathrm{Factor\:out\:}m\mathrm{\:from\:}m^2-23m \\\\\mathrm{Factor\:out\:}25\mathrm{\:from\:}25m-575\\\\m\left(m-23\right)+25\left(m-23\right) = 0\\\\\mathrm{Factor\:out\:common\:term\:}m-23\\\\\left(m-23\right)\left(m+25\right) = 0\\\\m = 23\\\\m = -25\ ignore\ negative\ value$

Thus the numbers are:

m = 23

m + 2 = 23 + 2 = 25

Find LCM of 23 and 25

List all prime factors for each number.

Prime Factorization of 23 shows:    23 is prime

Prime Factorization of 25 is:    5 x 5  

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

5, 5, 23

Multiply these factors together to find the LCM

LCM = 5 x 5 x 23 = 575

Thus LCM is 575

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