Find an odd natural number x such that LCM(x,40)=1400
To find an odd natural number x such that LCM(x, 40) = 1400, we can start by factoring the numbers 40 and 1400 into their prime factors.
The prime factorization of 40 is 2^3 * 5^1, and the prime factorization of 1400 is 2^3 * 5^2 * 7^1.
The least common multiple (LCM) is found by taking the highest power of each prime factor that appears in either number.
Here, the highest power of 2 is 2^3, the highest power of 5 is 5^2, and the highest power of 7 is 7^1.
To find an odd natural number x such that LCM(x, 40) = 1400, we need to include an additional factor of 7 in x but not any additional factors of 2 or 5.
Therefore, one possible value for x is 7 * 1 = 7.
Hence, the odd natural number x that satisfies LCM(x, 40) = 1400 is x = 7.