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Three numbers are in the ratio 3:4:5 and their LCM is 2400.their HCF is?
- a)40
- b)80
- c)120
- d)200
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Three numbers are in the ratio 3:4:5 and their LCM is 2400.their HCF i...
Let nos. = 3x, 4x, 5x 60x ≡ 2400
So (3 x 40), (4 x 40), (5 x 40)
H.C.F = 40
So (3 x 40), (4 x 40), (5 x 40)
H.C.F = 40
Most Upvoted Answer
Three numbers are in the ratio 3:4:5 and their LCM is 2400.their HCF i...
Solution:
Given: Three numbers are in the ratio 3:4:5 and their LCM is 2400.
Step 1: Find the numbers
Let the three numbers be 3x, 4x, and 5x (where x is a common factor).
The LCM of 3x, 4x, and 5x is given as 2400.
So, 3x * 4x * 5x = 2400
=> 60x^3 = 2400
=> x^3 = 40
=> x = 40^(1/3)
=> x = 2 * 2 * 2 = 8
Therefore, the three numbers are:
3x = 3 * 8 = 24
4x = 4 * 8 = 32
5x = 5 * 8 = 40
So, the three numbers are 24, 32, and 40.
Step 2: Find the HCF
To find the HCF of the three numbers, we need to find the common factors of the three numbers.
The common factors of 24, 32, and 40 are 1, 2, 4, 8.
Therefore, the HCF of the three numbers is 8.
Therefore, the correct answer is option A) 40.
Given: Three numbers are in the ratio 3:4:5 and their LCM is 2400.
Step 1: Find the numbers
Let the three numbers be 3x, 4x, and 5x (where x is a common factor).
The LCM of 3x, 4x, and 5x is given as 2400.
So, 3x * 4x * 5x = 2400
=> 60x^3 = 2400
=> x^3 = 40
=> x = 40^(1/3)
=> x = 2 * 2 * 2 = 8
Therefore, the three numbers are:
3x = 3 * 8 = 24
4x = 4 * 8 = 32
5x = 5 * 8 = 40
So, the three numbers are 24, 32, and 40.
Step 2: Find the HCF
To find the HCF of the three numbers, we need to find the common factors of the three numbers.
The common factors of 24, 32, and 40 are 1, 2, 4, 8.
Therefore, the HCF of the three numbers is 8.
Therefore, the correct answer is option A) 40.
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Three numbers are in the ratio 3:4:5 and their LCM is 2400.their HCF is?a)40b)80c)120d)200Correct answer is option 'A'. Can you explain this answer?
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