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Sum of two positive integers is 10 while their product is 24 What is the LCM of these numbers ?
- a)12
- b)24
- c)6
- d)4
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Sum of two positive integers is 10 while their product is 24 What is t...
If the numbers are x and y, xy = 24
x + y =10
So, the individual numbers are 4, 6
LCM of 4 and 6 = 12
Most Upvoted Answer
Sum of two positive integers is 10 while their product is 24 What is t...
To find the LCM (Least Common Multiple) of two numbers, we need to first determine the prime factors of each number.
Given that the sum of two positive integers is 10, we can assume the two numbers are x and y, where x + y = 10.
Additionally, we know that the product of these two numbers is 24, so xy = 24.
We can use these equations to solve for x and y. Here's one way to do it:
1. Solve for y in terms of x in the first equation:
y = 10 - x
2. Substitute the value of y in the second equation:
x(10 - x) = 24
3. Simplify the equation:
10x - x^2 = 24
4. Rearrange the equation:
x^2 - 10x + 24 = 0
5. Factorize the quadratic equation:
(x - 6)(x - 4) = 0
6. Set each factor equal to zero and solve for x:
x - 6 = 0 or x - 4 = 0
x = 6 or x = 4
So, the two numbers are either 4 and 6 or 6 and 4.
Now, let's find the prime factors of each number:
For 4:
4 = 2^2
For 6:
6 = 2 * 3
To find the LCM, we need to consider the highest power of each prime factor that appears in either number. In this case, the highest power of 2 is 2^2 and the highest power of 3 is 3^1.
Therefore, the LCM of 4 and 6 is:
LCM(4, 6) = 2^2 * 3^1 = 12.
Hence, the correct answer is option 'A' - 12.
Given that the sum of two positive integers is 10, we can assume the two numbers are x and y, where x + y = 10.
Additionally, we know that the product of these two numbers is 24, so xy = 24.
We can use these equations to solve for x and y. Here's one way to do it:
1. Solve for y in terms of x in the first equation:
y = 10 - x
2. Substitute the value of y in the second equation:
x(10 - x) = 24
3. Simplify the equation:
10x - x^2 = 24
4. Rearrange the equation:
x^2 - 10x + 24 = 0
5. Factorize the quadratic equation:
(x - 6)(x - 4) = 0
6. Set each factor equal to zero and solve for x:
x - 6 = 0 or x - 4 = 0
x = 6 or x = 4
So, the two numbers are either 4 and 6 or 6 and 4.
Now, let's find the prime factors of each number:
For 4:
4 = 2^2
For 6:
6 = 2 * 3
To find the LCM, we need to consider the highest power of each prime factor that appears in either number. In this case, the highest power of 2 is 2^2 and the highest power of 3 is 3^1.
Therefore, the LCM of 4 and 6 is:
LCM(4, 6) = 2^2 * 3^1 = 12.
Hence, the correct answer is option 'A' - 12.
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Sum of two positive integers is 10 while their product is 24 What is the LCM of these numbers ?a)12b)24c)6d)4Correct answer is option 'A'. Can you explain this answer?
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