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The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
- a)276
- b)299
- c)322
- d)345
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The H.C.F. of two numbers is 23 and the other two factors of their L.C...
Clearly, the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Most Upvoted Answer
The H.C.F. of two numbers is 23 and the other two factors of their L.C...
Given: H.C.F. = 23, L.C.M. factors = 13, 14
To find: Larger of two numbers
Let the two numbers be x and y
Hence, we can write:
x = 23a, y = 23b, where a and b are co-prime
L.C.M. of x and y = 23*13*14
We know that L.C.M. * H.C.F. = x * y
So, we can write:
23*13*14*23 = x * y * 23
x * y = 23^2 * 13 * 14
Now, we have two equations:
x = 23a, y = 23b
x * y = 23^2 * 13 * 14
Substituting the values, we get:
23a * 23b = 23^2 * 13 * 14
a * b = 23 * 13 * 14
Now, since a and b are co-prime, they must be 13 and 14 in some order.
If a = 13 and b = 14, then x = 23a = 23*13 = 299 and y = 23b = 23*14 = 322
If a = 14 and b = 13, then x = 23a = 23*14 = 322 and y = 23b = 23*13 = 299
Hence, the larger of the two numbers is 322.
To find: Larger of two numbers
Let the two numbers be x and y
Hence, we can write:
x = 23a, y = 23b, where a and b are co-prime
L.C.M. of x and y = 23*13*14
We know that L.C.M. * H.C.F. = x * y
So, we can write:
23*13*14*23 = x * y * 23
x * y = 23^2 * 13 * 14
Now, we have two equations:
x = 23a, y = 23b
x * y = 23^2 * 13 * 14
Substituting the values, we get:
23a * 23b = 23^2 * 13 * 14
a * b = 23 * 13 * 14
Now, since a and b are co-prime, they must be 13 and 14 in some order.
If a = 13 and b = 14, then x = 23a = 23*13 = 299 and y = 23b = 23*14 = 322
If a = 14 and b = 13, then x = 23a = 23*14 = 322 and y = 23b = 23*13 = 299
Hence, the larger of the two numbers is 322.
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The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:a)276b)299c)322d)345Correct answer is option 'C'. Can you explain this answer?
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The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:a)276b)299c)322d)345Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:a)276b)299c)322d)345Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:a)276b)299c)322d)345Correct answer is option 'C'. Can you explain this answer?.
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