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