Question

Product of two consecutive odd number is 575. Find their LCM

Answer 1

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

Answer 2

LET'S THE TWO NUMBERS ARE

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]