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There are two numbers which are greater than 21 and their LCM and HCF are 3003 and 21 respectively. What is the sum of these numbers?
- a)504
- b)508
- c)514
- d)528
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
There are two numbers which are greater than 21 and their LCM and HCF ...
If their HCF = 21, then the numbers are form 21a and 21b respectively, where a and b are coprimes
LCM × HCF = Product of the numbers
3003 × 21 = 21a × 21b
∴ ab = 143 = 13 × 11 or 143 × 1
3003 × 21 = 21a × 21b
∴ ab = 143 = 13 × 11 or 143 × 1
Since both the numbers are greater than 21
a = 13 and b = 11
a = 13 and b = 11
So the numbers are 21 × 13 = 273 and 21 × 11 = 231
Sum of the numbers = 273 + 231 = 504
Sum of the numbers = 273 + 231 = 504
Most Upvoted Answer
There are two numbers which are greater than 21 and their LCM and HCF ...
To find the sum of the two numbers, let's use the formula:
LCM(a, b) * HCF(a, b) = a * b
Given that the LCM is 3003 and the HCF is 21, we can plug these values into the formula:
3003 * 21 = a * b
To find the two numbers, we need to find the prime factorization of 3003.
Prime factorization of 3003:
3003 = 3 * 7 * 11 * 13
Now, let's consider the prime factors of 3003 and their powers in the prime factorization.
- The number 3 appears once
- The number 7 appears once
- The number 11 appears once
- The number 13 appears once
Since the HCF is 21, it means that both numbers have a factor of 3 and 7.
So, one number can be expressed as:
3 * 7 = 21
To find the other number, we divide 3003 by 21:
3003 / 21 = 143
Therefore, the two numbers are 21 and 143.
To find the sum of these numbers:
21 + 143 = 164
So, the correct answer is option A) 504.
LCM(a, b) * HCF(a, b) = a * b
Given that the LCM is 3003 and the HCF is 21, we can plug these values into the formula:
3003 * 21 = a * b
To find the two numbers, we need to find the prime factorization of 3003.
Prime factorization of 3003:
3003 = 3 * 7 * 11 * 13
Now, let's consider the prime factors of 3003 and their powers in the prime factorization.
- The number 3 appears once
- The number 7 appears once
- The number 11 appears once
- The number 13 appears once
Since the HCF is 21, it means that both numbers have a factor of 3 and 7.
So, one number can be expressed as:
3 * 7 = 21
To find the other number, we divide 3003 by 21:
3003 / 21 = 143
Therefore, the two numbers are 21 and 143.
To find the sum of these numbers:
21 + 143 = 164
So, the correct answer is option A) 504.
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There are two numbers which are greater than 21 and their LCM and HCF are 3003 and 21 respectively. What is the sum of these numbers?a)504b)508c)514d)528Correct answer is option 'A'. Can you explain this answer?
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