LCM & HCF
Highest Common Factor (HCF) and Least Common Multiple (LCM) are two fundamental building blocks of mathematics. HCF is also known as the Greatest Common Divisor (GCD). It is defined as the largest number that divides two or more given numbers perfectly without leaving any remainder. To understand this, consider the numbers 12 and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. Looking at both lists, the common factors are 1, 2, 3, and 6.
Concepts (3)
When dealing with fractions, you cannot find common factors directly. You must use a specific formula. For HCF, find the HCF of the top numbers and the LCM of the bottom numbers.
When dealing with fractions, you cannot find common factors directly. You must use a specific formula. For HCF, find the HCF of the top numbers and the LCM of the bottom numbers. For LCM, do the opposite: find the LCM of the top numbers and the HCF of the bottom numbers. Example: For 1/2 and 3/4, the LCM is LCM(1,3)/HCF(2,4), which is 3/2.
This method involves breaking down each number into its prime factors. To find HCF, multiply the lowest power of all common prime factors. To find LCM, multiply the highest power of every prime factor present in any of the numbers.
This method involves breaking down each number into its prime factors. To find HCF, multiply the lowest power of all common prime factors. To find LCM, multiply the highest power of every prime factor present in any of the numbers. Example: 12 is (2^2 × 3) and 18 is (2 × 3^2). HCF is (2^1 × 3^1) = 6. LCM is (2^2 × 3^2) = 36.
This is the most important formula for competitive exams. It states that for any two numbers A and B, the result of multiplying their HCF and LCM is equal to multiplying A and B.
This is the most important formula for competitive exams. It states that for any two numbers A and B, the result of multiplying their HCF and LCM is equal to multiplying A and B. This allows you to find a missing number if the other three values are known. Example: If HCF is 4, LCM is 24, and one number is 8, the other number is (4 × 24) / 8 = 12.
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Start Lesson: HCF and LCM of Fractions