Visualize an abstract mathematical concept. There is an equation balanced on an antique wooden scale. On the left side of the scale is an odd natural number depicted as a series of green dots. On the right side, a digital number '40' glows softly. A beam of light connects these numbers, and an equation emerges from the beam, showing LCM(x, 40) equals to 1400, which is depicted as a broad golden number. The scene is set within a serene study with a chalkboard, bookshelves, and a parchment themed background.

Find the value of an odd natural number x if LCM(x, 40)=1400

The LCM of x and 40 is 1400

x is odd. tale the prime factorization.
1400 = 7 × 2 × 2 × 2 × 5 × 5
40 = 5 × 2 × 2 × 2
The common factors of both 1400 and 40 are: 5 × 2 × 2 × 2
= 40, which means the
GCD is 40
if GCD is 40 then other number is 1400
as if smallest number divides greater number then smaller number is GCD and greater number is LCM.
However, this is impossible since 1400 is even. Therefore,
1400/40 = 35
if other number is 35,
then LCM of 40 and 35 is 280
1400/280 = 5
so other number is 35 × 5 = 175
175 = 5 × 5 × 7
40 = 5 × 8
LCM = 5 × 5 × 7 × 8 = 1400
so x = 175

To Find The Value Of 'X' First LCM (X,40)=1400 Then LCM 1/40 (X,40)= 1/40(1400) X=35 Then LCM (35,40) 35=35,70,105,140,175,210,245,280 40=40,80,120,160,200,240,280 The LCM(35,40)=280 Then The LCM Of (X,40) Divided By LCM Of (35,40) &Multiply By '35' Is Equals To The Value Of 'X' Then 1400/280=5 & 5*35=175 then the value of 'x' is equals to 175 x=175

175

The answer is simple:

First, let's divide 1400 by 40
We get 35, then insert it in x i.e. (35, 40)
Find the LCM of (35, 40) which is 280
Divide 1400 to 280 the result will be 5
Then, multiply 5 & 35, the answer will be 175

x=2n+1,40=2^3*5,then( 2n+1)*40=1400,n =17,so, x=35 again GCF(35,40)=5 ,so the odd natural number is y =35*5=175

No answer, am confused ????sorry

x must divide 1400, which is 2*7*2*5*2*5

Can you make a guess now?

40=2*2*2*5 1400=2*2*2*5*5*7 X= 5*5*7

Simply x=175

The answer is 175