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LCM and HCF Concepts
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LCM and HCF Concepts

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Questions and Answers

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

  • 72 (correct)
  • 60
  • 120
  • 90
  • Which of the following statements is true about the LCM and HCF of two numbers?

  • HCF is always greater than LCM
  • LCM and HCF are always equal
  • LCM is always greater than HCF (correct)
  • The product of LCM and HCF is equal to the sum of the numbers
  • If the LCM of two numbers is 48 and their HCF is 4, what is their product?

  • 448
  • 192 (correct)
  • 256
  • 576
  • What is the HCF of 24 and 36, if their prime factorizations are 24 = 2^3 × 3 and 36 = 2^2 × 3^2?

    <p>6</p> Signup and view all the answers

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

    <p>10</p> Signup and view all the answers

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

    <p>LCM and HCF are commutative and associative</p> Signup and view all the answers

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

    <p>180</p> Signup and view all the answers

    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:
      1. Find the prime factors of each number.
      2. Identify the common prime factors.
      3. 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) × HCF(a, b) = a × 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) × HCF(a, b) = a × 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.

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