Find an even number x such that lcm x40-1400
To find an even number that meets the given condition, we need to find a number that is a multiple of both 40 and 1400.
First, we find the least common multiple (LCM) of 40 and 1400. To do this, we factorize both numbers:
40 = 2^3 * 5
1400 = 2^3 * 5^2 * 7
Next, we take the highest power of each prime factor that appears in either number:
2^3, 5^2, 7
Finally, we multiply these prime factors together to find the LCM:
LCM = 2^3 * 5^2 * 7 = 280
Therefore, any even multiple of 280 will satisfy the given condition. For example, x = 2 * 280 = 560.