HCF & LCM

What is a factor?

A factor is a number that divides exactly into another number without leaving a remainder.

What is a multiple?

A multiple is a result of multiplying a number by a natural number.

What is the Highest Common Factor (HCF)?

The Highest Common Factor (HCF) is the largest common factor between two or more numbers.

What is the Ladder Method for finding the HCF?

1. Write each number as a product of its prime factors (prime factorization). 2. Write the prime factorizations above one another in matching pairs. 3. Circle the matching prime factors. 4. Multiply the matching prime factors (one per pair) to find the HCF.

What is the Lowest Common Multiple (LCM)?

The Lowest Common Multiple (LCM) is the lowest common multiple between two or more numbers.

What is the Ladder Method for finding the LCM?

1. Write each number as a product of its prime factors (prime factorization). 2. Write the prime factorizations above one another and pair where possible. 3. Circle the unpaired numbers individually. 4. Multiply the paired prime factors (one per pair) to find the LCM.

Why is prime factorization important for finding HCF and LCM?

Prime factorization is important because it breaks down numbers into their basic building blocks (prime numbers), allowing for an easier way to see commonalities for HCF and multiples for LCM.

What does LCM stand for?

LCM stands for Least Common Multiple, which is the smallest positive integer that is divisible by two or more given numbers.

How do you find the LCM of two numbers using prime factorization?

To find the LCM using prime factorization, follow these steps: 1. Break down each number into its prime factors. 2. Identify all unique prime factors from the numbers. 3. For each unique prime factor, take the highest power that appears in the factorization of either number. 4. Multiply these together to get the LCM.

Explain why the LCM is important when adding fractions with different denominators.

The LCM is important when adding fractions because it allows us to find a common denominator. To add fractions, the denominators need to be the same, and the LCM of the denominators gives us the smallest common denominator to work with.

In practical applications, why is finding the LCM significant?

Finding the LCM is significant in various real-world scenarios, such as scheduling events that occur at different intervals, determining common time frames for tasks, optimizing systems in telecommunications, and in the calculation and addition of fractions in mathematics.