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The Magic of HCF and LCM
What are HCF and LCM?
HCF (Highest Common Factor): The HCF of two or more numbers is the largest number that divides each of the numbers without leaving a remainder. It’s the greatest common divisor of the numbers.
LCM (Lowest Common Multiple): The LCM of two or more numbers is the smallest number that is a multiple of each of the numbers. It’s the smallest number that both numbers divide evenly into.
The HCF is the product of all the common prime factors of the given numbers. Example: HCF(36, 60) Prime factorization of 36: 2² × 3² Prime factorization of 60: 2² × 3 × 5 Common factors: 2² × 3 = 12, so HCF = 12
2. Dividing Objects into Equal Parts
If you have a set of items and need to divide them into groups, HCF helps you find the largest number of equal groups that can be made.
- Example 2: Divide 36 apples and 48 oranges into equal-sized boxes:
- Solution: The HCF of 36 and 48 is 12. So, you can make 12 boxes with equal numbers of apples and oranges.