Find an odd natural number x such that LCM (x, 40) = 1400

Answer 1

For 40 the prime factorization is:

2³ ∙ 5¹

For 1400 the prime factorization is:

2³ ∙ 5² ∙ 7¹

Since x is an odd number, the factor 2³ must be discarded.

The number x can be written as:

x = 5ᵐ ∙ 7ⁿ

where

m ≤ 2

because in factorization the largest exponent of the number 5 is two

n ≤ 1

because in factorization the largest exponent of the number 7 is one

By testing these values you get:

For m = 0 , n = 0

x = 5⁰ ∙ 7⁰ = 1 ∙ 1 = 1

LCM of 1 and 40 is 40

For m = 0 , n = 1

x = 5⁰ ∙ 7¹ = 1 ∙ 7 = 7

LCM of 7 and 40 is 280

For m = 1 , n = 0

x = 5¹ ∙ 7⁰ = 5 ∙ 1 = 5

LCM of 5 and 40 is 40

For m = 1 , n = 1

x = 5¹ ∙ 7¹ = 5 ∙ 7 = 35

LCM of 35 and 40 is 280

For m = 2 , n = 0

x = 5² ∙ 7⁰ = 25 ∙ 1 = 25

LCM of 25 and 40 is 200

For m = 2 , n = 1

x = 5² ∙ 7¹ = 25 ∙ 7 = 175

LCM of 175 and 40 is 1400

So x = 175

Answer 2

INTERESTING

Answer 3

it is very compiecatid try to esay it

Answer 4

odd means = 2n +1
then 1400 = 40x = 40( 2n + 1)
then 1400/40 = x/2n + 1
35 = x/2n +1
x = 35(2n + 1)
test n with small number start from 0
n = 0 - - - - - - - - x = 35 it does't give 1400 when we take LCM
n = 1 -------- ------ x = 105 it satisfy all the property
n = 2 ---------------x = 175 " " " " " " "