# Find the value of an odd natural number x if Lcm (x 40) =1400

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

40 = 2^3 * 5
so x = 5^2 * 7 = 175

## To find the value of an odd natural number x if LCM (x, 40) = 1400, you need to determine the prime factors of 1400 and then identify the appropriate factors for x.

Step 1: Prime factorize 1400:
The prime factors of 1400 are 2, 2, 2, 5, 5, 7.

Step 2: Determine the prime factors needed for x:
Since x is an odd natural number, it should not divide evenly by 2. Therefore, we need the prime factors of 5 and 7.

Step 3: Calculate the value of x:
Multiply the prime factors of 5 and 7 to find the value of x:
x = 5 * 7 = 35.

So, the value of the odd natural number x is 35 in order to have LCM (x, 40) = 1400.

## To find the value of an odd natural number x if LCM (x, 40) = 1400, we need to find the least common multiple (LCM) of x and 40.

The LCM of two numbers is the smallest multiple that both numbers divide into evenly.

First, we prime factorize the number 40: 40 = 2^3 * 5

Now, let's express the LCM as a product of prime factors. The LCM (x, 40) = 1400 can be prime factorized as follows: 1400 = 2^3 * 5^2 * 7.

To find the value of x, we need to compare the prime factorizations of 1400 and 40.

Comparing the powers of 2, we see that 1400 has a higher power of 2 (3) than 40 (1). Therefore, x must have at least a power of 2 equal to 3.

Next, comparing the powers of 5, we see that 1400 has a lower power of 5 (0) than 40 (1). Therefore, x must have at least a power of 5 equal to 1.

Finally, comparing the powers of 7, we see that 1400 has a higher power of 7 (1) than 40 (0). Therefore, x must have at least a power of 7 equal to 1.

Thus, the prime factorization of x can be written as x = 2^3 * 5^1 * 7^1 = 280.

Therefore, the value of the odd natural number x is 280.