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The ratio of three numbers is 3:4:6 and their LCM is 36. What is the difference between the largest and the smallest number?
- a)6
- b)9
- c)12
- d)15
Correct answer is option 'B'. Can you explain this answer?
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The ratio of three numbers is 3:4:6 and their LCM is 36. What is the ...
Let the numbers be 3k, 4k and 6k respectively.
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LCM(3k, 4k, 6k) = 36
⇒ k*LCM(3, 4, 6) = 36
⇒ 12k = 36
⇒ k = 3
Difference between the largest and the smallest number = 6k - 3k = 3k = 9
Most Upvoted Answer
The ratio of three numbers is 3:4:6 and their LCM is 36. What is the ...
Given that the ratio of three numbers is 3:4:6, let's assume the numbers to be 3x, 4x, and 6x, where x is a constant.
The LCM of the three numbers can be found by finding the LCM of their individual factors. The factors of the numbers are as follows:
- For 3x: 3, x
- For 4x: 2, 2, x
- For 6x: 2, 3, x
Taking the maximum power of each prime factor, the LCM is given by 2^2 * 3 * x = 36.
Simplifying the equation, we have 12x = 36.
Dividing both sides by 12, we get x = 3.
Now, substitute the value of x back into the original equation to find the three numbers:
- The first number is 3x = 3 * 3 = 9.
- The second number is 4x = 4 * 3 = 12.
- The third number is 6x = 6 * 3 = 18.
The difference between the largest and smallest number is 18 - 9 = 9.
Therefore, the correct answer is option B) 9.
The LCM of the three numbers can be found by finding the LCM of their individual factors. The factors of the numbers are as follows:
- For 3x: 3, x
- For 4x: 2, 2, x
- For 6x: 2, 3, x
Taking the maximum power of each prime factor, the LCM is given by 2^2 * 3 * x = 36.
Simplifying the equation, we have 12x = 36.
Dividing both sides by 12, we get x = 3.
Now, substitute the value of x back into the original equation to find the three numbers:
- The first number is 3x = 3 * 3 = 9.
- The second number is 4x = 4 * 3 = 12.
- The third number is 6x = 6 * 3 = 18.
The difference between the largest and smallest number is 18 - 9 = 9.
Therefore, the correct answer is option B) 9.
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The ratio of three numbers is 3:4:6 and their LCM is 36. What is the difference between the largest and the smallest number?a)6b)9c)12d)15Correct answer is option 'B'. Can you explain this answer?
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