find odd natura number A such that lcm(A,40)equal to 1400
1400 = 200*7 = 2^3 * 5^2 * 7
40 = 2^3 * 5
But LCM(35,40) = 2^3*5*7 = 280
So, you want A = 5^2 * 7 = 175
X=175
To find an odd natural number A such that LCM(A, 40) is equal to 1400, we can use the definition of the least common multiple (LCM).
The LCM of two numbers is the smallest multiple that is divisible by both numbers. In this case, we want the LCM of A and 40 to be 1400.
We know that 1400 is divisible by 40, so we need to find a number A such that 1400 is divisible by A and the only common factors of A and 40 are powers of 2.
Let's start by finding the prime factorization of 1400 and 40:
1400 = 2^3 * 5^2 * 7
40 = 2^3 * 5
To ensure that the LCM of A and 40 is 1400, we need to have A divisible by the remaining prime factors of 1400, which is 7 in this case.
Therefore, A should be a multiple of 7. Since we want A to be an odd number, we can choose A = 7.
Now, let's check if A = 7 satisfies the condition:
LCM(7, 40) = (7 * 40) / GCD(7, 40) = 280 / 1 = 280
The LCM of 7 and 40 is indeed 280, not 1400. So, there is no odd number A that satisfies the given condition.