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

The odd natural number which is mentioned as X is 175.

Step-by-step explanation:

By prime Factorization method. Step 1 : The prime factor for 40 is = 2*2*2*5. Step 2 : The prime factor for 1400 is = 2*2*2*5*5*7. Step 3 : the prime factor for the unknown natural odd number is to be find by comparing the factors of 40 and 1400. Step 4 : Lcm is known as least common multiple. Step 5 : Thus we can see the 5*5*7 in 1400 as different factors from the factors of 40. Step 6 : So lets multiply the factors we get number 175 which satisfies the condition of the odd number. Step 7 : The prime factors of 175 are 5*5*7.