Find an odd natural number x such that LCM (x, 40) = 1400.
175
First 1400=2^3*5^2*7
40=2^3*5
Then we take non common one and common with the biggest power
x=2^3*5^2*7 can be one answer but the question says an odd number the other possible outcome would be x=5^2*7=175,this is because 2^3 had chance to be in x and also not to be in x.
1400=2^3×5^2×7
40=2^3×5
LCM(40,1400)=2^3×5^2×7
X=5^3×7(25×7)=175
X IS 175
40 = 2^3 * 5
1400 = 2^3 * 5^2 * 7
LCM(2^3 * 5, 5^2 * 7) = 1400
so x = 175
To find an odd natural number x such that the least common multiple (LCM) of x and 40 is 1400, we can use the properties of LCM.
First, let's find the prime factorization of 1400 and 40.
Prime factorization of 1400:
1400 = 2^3 * 5^2 * 7
Prime factorization of 40:
40 = 2^3 * 5
Now, let's determine the LCM.
LCM(x, 40) is the product of the highest powers of all the prime factors of x and 40.
From the prime factorization of 1400 and 40, we can see that the highest powers of the prime factors are:
- 2^3 (since there are 3 twos in the prime factorization of 1400, and 3 twos in the prime factorization of 40)
- 5^2 (since there are 2 fives in the prime factorization of 1400, and 1 five in the prime factorization of 40)
- 7 (since there is 1 seven in the prime factorization of 1400, and no sevens in the prime factorization of 40)
To get the LCM, we multiply these highest powers:
LCM(x, 40) = 2^3 * 5^2 * 7 = 280
Now, we need to find an odd natural number x such that LCM(x, 40) = 280.
Since 280 is an even number, we cannot find an odd natural number that satisfies this condition.