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Two numbers are in ratio 4 : 5 and their HCF is 13. Their LCM is:
- a)260
- b)52
- c)65
- d)265
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two numbers are in ratio 4 : 5 and their HCF is 13. Their LCM is:a)260...
Let the two numbers be 4x and 5x respectively.
The HCF of 4x and 5x is x.
⇒ x = 13
We know that,
Product of two numbers x and y = LCM(x, y) × HCF(x, y)
⇒ 4 × 13 × 5 × 13 = LCM × 13
⇒ LCM = 260
∴ LCM = 260
The HCF of 4x and 5x is x.
⇒ x = 13
We know that,
Product of two numbers x and y = LCM(x, y) × HCF(x, y)
⇒ 4 × 13 × 5 × 13 = LCM × 13
⇒ LCM = 260
∴ LCM = 260
Most Upvoted Answer
Two numbers are in ratio 4 : 5 and their HCF is 13. Their LCM is:a)260...
To find the least common multiple (LCM) of two numbers, we need to first find their highest common factor (HCF) or greatest common divisor (GCD). In this question, we are given the ratio of the two numbers as 4:5 and their HCF as 13.
Let's assume the two numbers as 4x and 5x, where x is a common factor. We are given that the HCF of these numbers is 13. This means that 13 is the largest number that divides both 4x and 5x.
So, we can write the numbers as 4x = 13a and 5x = 13b, where a and b are co-prime numbers (i.e., they don't have any common factors other than 1).
Finding the LCM:
The LCM of two numbers is the product of the numbers divided by their HCF. In this case, the LCM of 4x and 5x can be calculated as:
LCM(4x, 5x) = (4x * 5x) / HCF(4x, 5x)
Substituting the values of 4x and 5x:
LCM(4x, 5x) = (4x * 5x) / 13
= (20x^2) / 13
Since x can be any positive integer, let's assume x = 13 to get the smallest possible value for the LCM:
LCM(4x, 5x) = (20x^2) / 13
= (20 * 13^2) / 13
= 20 * 13
= 260
Therefore, the LCM of the two numbers is 260. Hence, the correct answer is option A.
Let's assume the two numbers as 4x and 5x, where x is a common factor. We are given that the HCF of these numbers is 13. This means that 13 is the largest number that divides both 4x and 5x.
So, we can write the numbers as 4x = 13a and 5x = 13b, where a and b are co-prime numbers (i.e., they don't have any common factors other than 1).
Finding the LCM:
The LCM of two numbers is the product of the numbers divided by their HCF. In this case, the LCM of 4x and 5x can be calculated as:
LCM(4x, 5x) = (4x * 5x) / HCF(4x, 5x)
Substituting the values of 4x and 5x:
LCM(4x, 5x) = (4x * 5x) / 13
= (20x^2) / 13
Since x can be any positive integer, let's assume x = 13 to get the smallest possible value for the LCM:
LCM(4x, 5x) = (20x^2) / 13
= (20 * 13^2) / 13
= 20 * 13
= 260
Therefore, the LCM of the two numbers is 260. Hence, the correct answer is option A.
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Two numbers are in ratio 4 : 5 and their HCF is 13. Their LCM is:a)260b)52c)65d)265Correct answer is option 'A'. Can you explain this answer? for Railways 2025 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Two numbers are in ratio 4 : 5 and their HCF is 13. Their LCM is:a)260b)52c)65d)265Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two numbers are in ratio 4 : 5 and their HCF is 13. Their LCM is:a)260b)52c)65d)265Correct answer is option 'A'. Can you explain this answer?.
Two numbers are in ratio 4 : 5 and their HCF is 13. Their LCM is:a)260b)52c)65d)265Correct answer is option 'A'. Can you explain this answer? for Railways 2025 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Two numbers are in ratio 4 : 5 and their HCF is 13. Their LCM is:a)260b)52c)65d)265Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two numbers are in ratio 4 : 5 and their HCF is 13. Their LCM is:a)260b)52c)65d)265Correct answer is option 'A'. Can you explain this answer?.
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