Define x:
Let one number be x
The next odd consecutive number is x + 2
Form equation:
Their product is 575
⇒x (x + 2) = 575
Solve x:
x (x + 2) = 575
x² + 2x = 575
x² + 2x - 575 = 0
(x + 25)(x - 23) = 0
x = -25 or x = 23
Find the number pairs:
if x = -25, x + 2 = -23
∴ the numbers are -23 and -25
If x = 23, x + 2 = 25
∴ the numbers are 23 and 25
Find the Prime factors of 23 and 25
23 = 23
25 = 5²
Find the LCM:
*The LCM is the same for both the positive or the negative pairs
Since there is no common factors,
LCM = 23 x 25 = 575
Answer: The LCM is 575
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Verified answer
Define x:
Let one number be x
The next odd consecutive number is x + 2
Form equation:
Their product is 575
⇒x (x + 2) = 575
Solve x:
x (x + 2) = 575
x² + 2x = 575
x² + 2x - 575 = 0
(x + 25)(x - 23) = 0
x = -25 or x = 23
Find the number pairs:
if x = -25, x + 2 = -23
∴ the numbers are -23 and -25
If x = 23, x + 2 = 25
∴ the numbers are 23 and 25
Find the Prime factors of 23 and 25
23 = 23
25 = 5²
Find the LCM:
*The LCM is the same for both the positive or the negative pairs
Since there is no common factors,
LCM = 23 x 25 = 575
Answer: The LCM is 575
X AND (X+2)
NOW
According to the question
=> X×(X+2) = 575
=> X² + 2X - 575 = 0
=> X² + 25X - 23X - 575 = 0
=> X(X+25) -23(X+25) = 0
=> (X-23)(X+25) = 0
__________
Then
=> X = 23
Or
=> X = -25
__________
We take "X = 23"
then
smaller odd number = 23
and
Larger odd number = 23+2 = 25
__________________
Now their LCM :-
=> 23×25 = 575
____________[ANSWER]