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.

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.

= `1400/40` = 35

if other number is 35, then LCM of 40 and 35 is 280, = `1400/28` = 5

so other number is 35 × 5 = 175

175 = 5 × 5 × 7

40 = 5 × 8

LCM = 5 × 5 × 7 × 8 = 1400

so x = 175

hence ,

The value of x is 175