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Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
- a)40
- b)80
- c)120
- d)200
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. T...
Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
Most Upvoted Answer
Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. T...
To find the H.C.F. (Highest Common Factor), we need to find the highest number that can divide all three numbers in the given ratio.
Given that the numbers are in the ratio of 3 : 4 : 5, we can assume them as 3x, 4x, and 5x, where x is a common factor.
Given that the L.C.M. (Least Common Multiple) is 2400, we can write the equation as:
L.C.M. = (3x)(4x)(5x) / H.C.F.
2400 = 60x^3 / H.C.F.
To find the H.C.F., we need to find the value of x that satisfies the above equation.
Simplifying the equation, we get:
H.C.F. = 60x^3 / 2400
H.C.F. = x^3 / 40
Since x is a common factor, it should be a factor of the H.C.F.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
To find the value of x, we need to find a cube of one of these factors that is divisible by 40.
The only cube that satisfies this condition is 2^3 = 8.
So, x = 8.
Substituting the value of x in the assumed numbers, we get:
First number = 3x = 3 * 8 = 24
Second number = 4x = 4 * 8 = 32
Third number = 5x = 5 * 8 = 40
Therefore, the H.C.F. of the three numbers is 8, which is option 'A'.
Given that the numbers are in the ratio of 3 : 4 : 5, we can assume them as 3x, 4x, and 5x, where x is a common factor.
Given that the L.C.M. (Least Common Multiple) is 2400, we can write the equation as:
L.C.M. = (3x)(4x)(5x) / H.C.F.
2400 = 60x^3 / H.C.F.
To find the H.C.F., we need to find the value of x that satisfies the above equation.
Simplifying the equation, we get:
H.C.F. = 60x^3 / 2400
H.C.F. = x^3 / 40
Since x is a common factor, it should be a factor of the H.C.F.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
To find the value of x, we need to find a cube of one of these factors that is divisible by 40.
The only cube that satisfies this condition is 2^3 = 8.
So, x = 8.
Substituting the value of x in the assumed numbers, we get:
First number = 3x = 3 * 8 = 24
Second number = 4x = 4 * 8 = 32
Third number = 5x = 5 * 8 = 40
Therefore, the H.C.F. of the three numbers is 8, which is option 'A'.
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Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:a)40b)80c)120d)200Correct answer is option 'A'. Can you explain this answer?
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