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The ratio of two numbers is 5 : 6 and their LCM is 480, then their HCF is?
- a)16
- b)96
- c)12
- d)240
- e)48
Correct answer is option 'A'. Can you explain this answer?
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The ratio of two numbers is 5 : 6 and their LCM is 480, then their HCF...
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The ratio of two numbers is 5 : 6 and their LCM is 480, then their HCF...
Given, the ratio of two numbers is 5:6 and their LCM is 480.
Step-by-step solution:
Let the two numbers be 5x and 6x, where x is a positive integer.
LCM of two numbers = product of two numbers/HCF of two numbers.
LCM = 480 = (5x × 6x)/HCF
HCF = (5x × 6x)/480
HCF = x
Therefore, the HCF of the two numbers is x.
Since x is a factor of both 5x and 6x, x must be a factor of their HCF.
The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, and 480.
Out of these factors, only 16 is a factor of both 5 and 6.
Therefore, the HCF of the two numbers is 16.
Hence, option A, 16, is the correct answer.
Step-by-step solution:
Let the two numbers be 5x and 6x, where x is a positive integer.
LCM of two numbers = product of two numbers/HCF of two numbers.
LCM = 480 = (5x × 6x)/HCF
HCF = (5x × 6x)/480
HCF = x
Therefore, the HCF of the two numbers is x.
Since x is a factor of both 5x and 6x, x must be a factor of their HCF.
The factors of 480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, and 480.
Out of these factors, only 16 is a factor of both 5 and 6.
Therefore, the HCF of the two numbers is 16.
Hence, option A, 16, is the correct answer.
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The ratio of two numbers is 5 : 6 and their LCM is 480, then their HCF is?a)16b)96c)12d)240e)48Correct answer is option 'A'. Can you explain this answer?
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