Maths( HCF and LCM)

• What does LCM stand for in mathematics?

  LCM stands for Lowest Common Multiple.
• What is the definition of LCM?

  LCM is the smallest positive integer that is divisible by each of the numbers.
• What is the definition of HCF?

  HCF is the largest positive integer that divides each of the numbers without a remainder.
• What does HCF stand for in mathematics?

  HCF stands for Highest Common Factor.
• What is the HCF of 12 and 18?

  The HCF of 12 and 18 is 6.
• What is the LCM of 12 and 18?

  The LCM of 12 and 18 is 36.
• How can you think of HCF in simpler terms?

  HCF is the largest number that can divide into two or more numbers exactly without a remainder.
• How can you think of LCM in simpler terms?

  LCM is the smallest number that both of your original numbers can divide into exactly.
• What is the HCF of 4 and 6?

  The HCF of 4 and 6 is 2.
• What is the LCM of 4 and 6?

  The LCM of 4 and 6 is 12.
• What is the first step in finding the HCF using the listing factors method?

  List all factors of each number.
• What do you do after listing the factors to find the HCF?

  Identify the common factors.
• What is the HCF of 18 and 24 using the listing factors method?

  The HCF of 18 and 24 is 6.
• Why is the listing factors method effective for finding HCF?

  It is straightforward and easy to understand for smaller numbers.
• What is the first step in finding the LCM using the listing multiples method?

  List the multiples of each number.
• What do you do after listing the multiples to find the LCM?


  The first common multiple you find is the LCM.
• What is the LCM of 4 and 6 using the listing multiples method?

  The LCM of 4 and 6 is 12.
• Why is the listing multiples method effective for finding LCM?

  It is straightforward and easy to understand for smaller numbers.
• What is prime factorization?

  Prime factorization means breaking a number into its prime number building blocks.
• How do you find the HCF using prime factorization?

  Take the common prime factors with the lowest exponents.
• How do you find the LCM using prime factorization?

  Take all prime factors with the highest exponents.
• What is the HCF of 24 and 36 using prime factorization?

  The HCF of 24 and 36 is 12.
• What is the LCM of 24 and 36 using prime factorization?

  The LCM of 24 and 36 is 72.
• Why is prime factorization a more efficient method for finding HCF and LCM?

  It is especially useful for larger numbers and reduces the time needed to find factors or multiples.
• What are the steps to find the HCF using the listing factors method?

  1. List all factors of each number. 2. Identify the common factors. 3. Choose the largest common factor as the HCF.
• What are the steps to find the LCM using the listing multiples method?

  1. List the multiples of each number. 2. Identify the first common multiple. 3. The first common multiple is the LCM.
• What are the steps to find HCF and LCM using prime factorization?

  1. Break down each number into its prime factors. 2. For HCF: Take all common prime factors with the lowest exponents. 3. For LCM: Take all prime factors with the highest exponents.
• What is the result of the equation \(3^2 = 72\)?

  It is incorrect; \(3^2 = 9\).
• What does prime factorization mean?

  - Breaking a number into its prime number building blocks.
• What is the prime factorization of 12?

  12 = 2^2 \times 3
• What is the prime factorization of 18?

  18 = 2 \times 3^2
• How do you calculate the HCF of 12 and 18 using their prime factors?

  HCF = 2^1 \times 3^1 = 6
• How do you calculate the LCM of 12 and 18 using their prime factors?

  LCM = 2^2 \times 3^2 = 36
• If 20 = 2^2 \times 5 and 30 = 2 \times 3 \times 5, what is their HCF?

  HCF = 2^1 \times 5^1 = 10
• If 12 = 2^2 \times 3 and 18 = 2 \times 3^2, what is their LCM?

  LCM = 2^2 \times 3^2 = 36