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The HCF of two numbers is 23 and their LCM is 1449. If one of the numbers is 161 what is the other?
- a)107
- b)117
- c)167
- d)207
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The HCF of two numbers is 23 and their LCM is 1449. If one of the numb...
HCF = 23
LCM = 1449
Let the two numbers be a and b. Let a = 161. We have to find b.
We know that
HCF(a,b) * LCM(a,b) = a*b
∴23 * 1449 = 161 * b
∴23*1449/161 = b
∴b = 23*9
∴b = 207
Thus, the other number is 207.
Most Upvoted Answer
The HCF of two numbers is 23 and their LCM is 1449. If one of the numb...
To find the other number, we can use the formula:
LCM × HCF = Product of the two numbers
Given that the HCF is 23 and the LCM is 1449, we can substitute these values into the formula:
1449 × 23 = Product of the two numbers
Therefore, the product of the two numbers is 33327.
We are also given that one of the numbers is 161. Let's call the other number x.
So, the equation becomes:
161 × x = 33327
To find the value of x, we can divide both sides of the equation by 161:
x = 33327 ÷ 161
Performing the division, we get:
x ≈ 207
Therefore, the other number is approximately 207.
Hence, the correct answer is option D) 207.
LCM × HCF = Product of the two numbers
Given that the HCF is 23 and the LCM is 1449, we can substitute these values into the formula:
1449 × 23 = Product of the two numbers
Therefore, the product of the two numbers is 33327.
We are also given that one of the numbers is 161. Let's call the other number x.
So, the equation becomes:
161 × x = 33327
To find the value of x, we can divide both sides of the equation by 161:
x = 33327 ÷ 161
Performing the division, we get:
x ≈ 207
Therefore, the other number is approximately 207.
Hence, the correct answer is option D) 207.
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