## Podcast Beta

## Questions and Answers

What is the LCM of two numbers, if their HCF is 6 and their product is 360?

Which of the following statements is true about the LCM and HCF of two numbers?

If the LCM of two numbers is 48 and their HCF is 4, what is their product?

What is the HCF of 24 and 36, if their prime factorizations are 24 = 2^3 Ã— 3 and 36 = 2^2 Ã— 3^2?

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If the LCM of two numbers is 120 and their product is 3600, what is their HCF?

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Which of the following is a property of the LCM and HCF of two numbers?

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What is the LCM of 12, 15, and 20, if their HCF is 3?

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## Study Notes

### Least Common Multiple (LCM)

- The LCM of two or more numbers is the smallest number that is a multiple of each of the numbers.
- To find the LCM, list the multiples of each number and identify the first number that appears in all lists.
- LCM can be calculated using the formula: LCM(a, b) = |a*b| / GCF(a, b), where GCF is the Greatest Common Factor (HCF).

### Highest Common Factor (HCF) or Greatest Common Divisor (GCD)

- The HCF of two or more numbers is the largest number that divides each of the numbers exactly without leaving a remainder.
- To find the HCF, list the factors of each number and identify the highest factor common to all numbers.
- HCF can be calculated using the prime factorization method:
- Find the prime factors of each number.
- Identify the common prime factors.
- Multiply the common prime factors to get the HCF.

### Key Properties

- The product of LCM and HCF of two numbers is equal to the product of the numbers themselves: LCM(a, b) Ã— HCF(a, b) = a Ã— b
- LCM and HCF are commutative: LCM(a, b) = LCM(b, a) and HCF(a, b) = HCF(b, a)
- LCM and HCF are associative: LCM(a, LCM(b, c)) = LCM(LCM(a, b), c) and HCF(a, HCF(b, c)) = HCF(HCF(a, b), c)

### Least Common Multiple (LCM)

- Least Common Multiple (LCM) is the smallest number that is a multiple of each of the given numbers.
- To find LCM, list the multiples of each number and identify the first number that appears in all lists.
- LCM formula: LCM(a, b) = |a*b| / GCF(a, b), where GCF is the Greatest Common Factor (HCF).

### Highest Common Factor (HCF) or Greatest Common Divisor (GCD)

- Highest Common Factor (HCF) is the largest number that divides each of the given numbers exactly without leaving a remainder.
- To find HCF, list the factors of each number and identify the highest factor common to all numbers.
- HCF calculation using prime factorization method:
- Find the prime factors of each number.
- Identify the common prime factors.
- Multiply the common prime factors to get the HCF.

### Key Properties

- Product of LCM and HCF of two numbers is equal to the product of the numbers themselves: LCM(a, b) Ã— HCF(a, b) = a Ã— b.
- LCM and HCF are commutative: LCM(a, b) = LCM(b, a) and HCF(a, b) = HCF(b, a).
- LCM and HCF are associative: LCM(a, LCM(b, c)) = LCM(LCM(a, b), c) and HCF(a, HCF(b, c)) = HCF(HCF(a, b), c).

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## Description

Learn about the concepts of Least Common Multiple (LCM) and Highest Common Factor (HCF) or Greatest Common Divisor (GCD), including their definitions and formulas.