## 1400 = 40*35 = 2^3 * 5^2 * 7

So, the only missing odd factor is 5

LCM(35*5,40) = LCM(175,40) = 1400

Steve
answered

6 years ago

6 years ago

So, the only missing odd factor is 5

LCM(35*5,40) = LCM(175,40) = 1400

Mintesnot
answered

3 years ago

3 years ago

Step-by-Step Bot
answered

1 year ago

1 year ago

Let's start with the prime factorization of 40:

40 = 2^3 * 5

Now, let's find the prime factorization of 1400:

1400 = 2^3 * 5^2 * 7

To find the LCM (least common multiple) of x and 40, we need to find the highest power of each prime factor in the factorization of 1400.

In the factorization of 1400, we only have 2^3 and 5^2, which means the highest power of 7 should be 0.

Therefore, the LCM of x and 40 should have the prime factors of 2^3 and 5^2. To have a LCM of 1400, the highest power of 2 should be 3, and the highest power of 5 should be 2.

Thus, the prime factorization of x would be x = 2^3 * 5^2.

Now, let's find the value of x:

x = 2^3 * 5^2

x = 8 * 25

x = 200

So, the value of the odd natural number x, for which LCM(x, 40) = 1400, is 200.

Explain Bot
answered

1 year ago

1 year ago

Prime factorization of 1400:

1400 = 2^3 * 5^2 * 7

Prime factorization of 40:

40 = 2^3 * 5

Since the LCM includes all the prime factors from both numbers, we can see that the LCM of x and 40 should have the same prime factors and at least the same exponents.

Comparing the prime factorization of 1400 and the LCM of x and 40:

LCM (x, 40) = 2^3 * 5^2 * 7

Now, we can determine the values of x by matching the prime factors and their exponents.

The highest power of 2 in x can be equal to or greater than the one in 1400 (2^3). Let's assume it is equal, so x has a factor of 2^3.

The highest power of 5 in x can also be equal to or greater than the one in 1400 (5^2). Let's assume it is equal, so x has a factor of 5^2.

Since x is an odd natural number, it cannot have 2 as its factor more than 3 times. Therefore, x cannot have a factor of 2^3.

Hence, there is no odd natural number x that satisfies LCM (x, 40) = 1400.