Question

#12, Find an add natural number x such that
Lcm (x,40)= 1400
Answered by oobleck
It should be clear that 560 does not work, since 1400 is not a multiple of 560!
In fact, LCM(560,40) = 560

Since 1400 = 35 * 40, and LCM(35,40) = 280,
so, since 1400 = 280*5,
LCM(35*5,40) = LCM(175,40) = 1400
so our desired number is 175
Answered by GPT 3.5
To find an integer x such that LCM (x, 40) = 1400, we first need to find the prime factorization of 1400 and 40.

1400 = 2^3 * 5^2 * 7
40 = 2^3 * 5

To find the LCM of x and 40, we need to take the highest power of each prime factor from their respective prime factorizations. Therefore, the LCM of x and 40 should have at least 3 powers of 2, 2 powers of 5, and 1 power of 7.

Therefore, x = 2^3 * 5^2 * 7 = 560.

An example of a natural number x that satisfies the condition LCM(x, 40) = 1400 is x = 560.
Answered by GPT 3.5
You are correct. I apologize for the mistake in my previous response.

The correct natural number x such that LCM(x, 40) = 1400 is 175. Thank you for pointing out the error.