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The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is
- a)12
- b)16
- c)24
- d)48
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. ...
Given:
- The ratio of two numbers is 3:4
- The H.C.F. (Highest Common Factor) of the two numbers is 4.
Let's denote the two numbers as 3x and 4x, where x is a common multiplier.
Since the H.C.F. of the two numbers is given as 4, x must be 4 (because H.C.F. is the highest common factor, and 4 is the common factor here).
So, the two numbers are:
- First number = 3×4=12
- Second number = 4×4=16
Now, let's calculate the L.C.M. (Least Common Multiple) of 12 and 16.
Method:
The L.C.M. of two numbers can be calculated using the formula:
LCM×HCF=Product of the numbers
So,
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The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. ...
Given, the ratio of two numbers is 3 : 4 and their H.C.F. is 4.
Let the two numbers be 3x and 4x, where x is a positive integer.
Their H.C.F. is 4, which means that 4 is a factor of both 3x and 4x. Therefore, x must be a multiple of 4.
Let x = 4k, where k is a positive integer.
Then, the two numbers are 3x = 3(4k) = 12k and 4x = 4(4k) = 16k.
Their L.C.M. is given by the product of the numbers divided by their H.C.F., i.e.,
L.C.M. = (12k x 16k)/4 = 48k^2
Since k is a positive integer, the L.C.M. is a multiple of 48.
Therefore, the correct answer is option D) 48.
Let the two numbers be 3x and 4x, where x is a positive integer.
Their H.C.F. is 4, which means that 4 is a factor of both 3x and 4x. Therefore, x must be a multiple of 4.
Let x = 4k, where k is a positive integer.
Then, the two numbers are 3x = 3(4k) = 12k and 4x = 4(4k) = 16k.
Their L.C.M. is given by the product of the numbers divided by their H.C.F., i.e.,
L.C.M. = (12k x 16k)/4 = 48k^2
Since k is a positive integer, the L.C.M. is a multiple of 48.
Therefore, the correct answer is option D) 48.
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The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. isa)12 b)16 c)24 d)48Correct answer is option 'D'. Can you explain this answer? for Quant 2026 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. isa)12 b)16 c)24 d)48Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. isa)12 b)16 c)24 d)48Correct answer is option 'D'. Can you explain this answer?.
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. isa)12 b)16 c)24 d)48Correct answer is option 'D'. Can you explain this answer? for Quant 2026 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. isa)12 b)16 c)24 d)48Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. isa)12 b)16 c)24 d)48Correct answer is option 'D'. Can you explain this answer?.
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