Another way to learn LCM and HCF

Learning Objectives Define prime factorization and perform it for given composite numbers. Find the Highest Common Factor (HCF) of two or more numbers using their prime factorization. Find the Least Common Multiple (LCM) of two or more numbers using their prime factorization. Explain the relationship between the product of two numbers, their HCF, and their LCM. Apply the prime factorization method to solve real-world problems involving HCF and LCM. Compare the efficiency of different methods for finding HCF and LCM. Ever wondered how many hotdogs and buns to buy for a party so there are no leftovers? 🌭🍔 Or how to tile a floor perfectly without cutting any tiles? These puzzles often involve finding common ground between numbers! In this lesson, we'll explore a powerfu...

TermDefinitionExample Prime NumberA natural number greater than 1 that has no positive divisors other than 1 and itself.2, 3, 5, 7, 11 are prime numbers. 4 is not prime because it can be divided by 2. Composite NumberA natural number greater than 1 that is not a prime number; it has more than two factors (including 1 and itself).4, 6, 8, 9, 10 are composite numbers. 6 can be divided by 1, 2, 3, and 6. Prime FactorizationThe process of expressing a composite number as a product of its prime factors.The prime factorization of 12 is $2 \times 2 \times 3$ or $2^2 \times 3$. Common FactorA number that divides two or more numbers without leaving a remainder.For 12 and 18, the factors of 12 are {1, 2, 3, 4, 6, 12} and factors of 18 are {1, 2, 3, 6, 9, 18}. The common factors are {1, 2, 3, 6}. Hi...

HCF using Prime Factorization To find the HCF of two or more numbers, express each number as a product of its prime factors. The HCF is the product of the common prime factors, each raised to the lowest power it appears in any of the factorizations. If $a = p_1^{e_1} p_2^{e_2} \ldots$ and $b = p_1^{f_1} p_2^{f_2} \ldots$, then $HCF(a, b) = p_1^{\min(e_1, f_1)} p_2^{\min(e_2, f_2)} \ldots$. This rule is used when you need to find the largest number that can divide all given numbers exactly. LCM using Prime Factorization To find the LCM of two or more numbers, express each number as a product of its prime factors. The LCM is the product of all unique prime factors (common and non-common), each raised to the highest power it appears in any of the factorizations. If $a = p_1^{e_...