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HCF and LCM Tips and Tricks for Government Exams
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FAQs on HCF and LCM Tips and Tricks for Government Exams
| 1. What is the difference between HCF and LCM? |  |
Ans. HCF (Highest Common Factor) refers to the largest number that divides two or more given numbers without leaving any remainder. On the other hand, LCM (Least Common Multiple) represents the smallest number that is divisible by two or more given numbers.
| 2. How can I find the HCF of two numbers? | |
Ans. To find the HCF of two numbers, you can use various methods such as prime factorization, division method, or Euclidean algorithm. The prime factorization method involves finding the prime factors of both numbers and then identifying their common factors. The division method involves repeatedly dividing the larger number by the smaller number until the remainder becomes zero. The last divisor will be the HCF.
| 3. How do I calculate the LCM of two or more numbers? | |
Ans. To calculate the LCM of two or more numbers, you can use methods like prime factorization, listing multiples, or the division method. The prime factorization method involves finding the prime factors of each number and then multiplying the highest power of each factor. The listing multiples method involves listing the multiples of each number until you find a common multiple. The division method involves repeatedly dividing the numbers by their common factors until you get a common quotient.
| 4. Can you give an example of finding the HCF and LCM of two numbers? | |
Ans. Sure! Let's find the HCF and LCM of 12 and 18.
To find the HCF, we can use the division method:
12 ÷ 18 = 0 remainder 12
18 ÷ 12 = 1 remainder 6
12 ÷ 6 = 2 remainder 0
The last divisor is 6, so the HCF of 12 and 18 is 6.
To find the LCM, we can use the prime factorization method:
12 = 2^2 × 3
18 = 2 × 3^2
Multiplying the highest power of each factor:
2^2 × 3^2 = 4 × 9 = 36
So, the LCM of 12 and 18 is 36.
| 5. Are there any shortcuts or tricks to find the HCF and LCM quickly? | |
Ans. Yes, there are a few tricks to find the HCF and LCM quickly. For the HCF, you can use the Euclidean algorithm, which involves dividing the larger number by the smaller number and repeating the process with the remainder until you get zero. The last non-zero remainder will be the HCF. For the LCM, you can use the shortcut of dividing the product of the two numbers by their HCF. This will give you the LCM directly.
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Dec 22, 2024 Last updated |
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