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The HCF of two numbers is 12 and their LCM is 72. If one of the two numbers is 24, then the other number is:
- a)72
- b)48
- c)36
- d)60
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The HCF of two numbers is 12 and their LCM is 72. If one of the two nu...
GIVEN:
HCF of two numbers = 12
LCM = 72
Ist number = 24
FORMULA USED:
HCF × LCM = product of two numbers
CALCULATION:
⇒ 12 × 72 = 24 × other number
∴ Other number = 36
Most Upvoted Answer
The HCF of two numbers is 12 and their LCM is 72. If one of the two nu...
The highest common factor (HCF) and least common multiple (LCM) of two numbers are important concepts in number theory. The HCF is the largest positive integer that divides both numbers without leaving a remainder, while the LCM is the smallest positive integer that is divisible by both numbers.
Given that the HCF of two numbers is 12 and the LCM is 72, we can use these values to find the other number when one of them is 24.
Let's solve the problem step by step:
Step 1: Find the second number
We know that the product of the HCF and LCM of two numbers is equal to the product of the two numbers. Using this property, we can write the equation:
HCF * LCM = Number 1 * Number 2
Substituting the given values, we have:
12 * 72 = 24 * Number 2
Simplifying the equation, we get:
864 = 24 * Number 2
Dividing both sides by 24, we find:
36 = Number 2
Therefore, the other number is 36.
Step 2: Verify the answer
To verify our answer, we can check if 36 is indeed the HCF of 24 and 36, and if the LCM of these two numbers is 72.
The HCF of 24 and 36 is 12, which matches the given value.
The LCM of 24 and 36 can be found by dividing their product by their HCF:
LCM = (24 * 36) / 12 = 72
Thus, the HCF is 12 and the LCM is 72, as given in the problem.
Conclusion:
Therefore, if one of the two numbers is 24, the other number is 36, which is option C.
Given that the HCF of two numbers is 12 and the LCM is 72, we can use these values to find the other number when one of them is 24.
Let's solve the problem step by step:
Step 1: Find the second number
We know that the product of the HCF and LCM of two numbers is equal to the product of the two numbers. Using this property, we can write the equation:
HCF * LCM = Number 1 * Number 2
Substituting the given values, we have:
12 * 72 = 24 * Number 2
Simplifying the equation, we get:
864 = 24 * Number 2
Dividing both sides by 24, we find:
36 = Number 2
Therefore, the other number is 36.
Step 2: Verify the answer
To verify our answer, we can check if 36 is indeed the HCF of 24 and 36, and if the LCM of these two numbers is 72.
The HCF of 24 and 36 is 12, which matches the given value.
The LCM of 24 and 36 can be found by dividing their product by their HCF:
LCM = (24 * 36) / 12 = 72
Thus, the HCF is 12 and the LCM is 72, as given in the problem.
Conclusion:
Therefore, if one of the two numbers is 24, the other number is 36, which is option C.
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The HCF of two numbers is 12 and their LCM is 72. If one of the two numbers is 24, then the other number is:a)72b)48c)36d)60Correct answer is option 'C'. Can you explain this answer?
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