WBBSE Notes For Class 6 Maths Chapter 1 Simplification Highest Common Factor And Lowest Common Multiple

by

Chapter 1 Simplification Highest Common Factor And Lowest Common Multiple

Important Definitions Related to HCF and LCM

Chapter 1 Highest Common Factor

Highest Common Factor:

A composite number has two or more factors.

Simplification Questions For Class 6

Definition:

  1. The H. C. F. or Highest Common Factor of two integral numbers is the highest (or greatest) among all the possible common factors of the two numbers.
  2. We consider two numbers 15 and 20.
  3. 15 = 1 x 3 x 5 i.e., the factors of 15 are 1, 3, 5, 15.
  4. 20 = 1 x 2 x 2 x 5, i.e., the factors of 20 are 1, 2, 4, 5, 10, 20.
  5. ∴ 15 and 20 have common factors 1, and 5.
  6. Among them, the highest common factor is 5. 
  7. So the H. C. F. of 15 and 20 5. 
  8. Again, 36 1 x 2 x 2 x 3 x 3 and 48 = 1 x 2 x 2 x 2 x 2 x 3.
  9. ∴ The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 and the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
  10. ∴ The common factors of 36 and 48 are 1, 2, 3, 4, 6, and 12.
  11. Among these factors, the highest common factor is 12.
  12. ∴ The H. C. F. of 36 and 48 = 12.
  13. There are two processes in which the H. C. F. of two numbers can be determined. These are:
    1. Resolution into prime factors and
    2    . Division process.
  14. In the illustrative examples below, both processes are described to determine the H. C. F. of two numbers.

WBBSE Notes For Class 6 Maths Chapter 1 Simplification Highest Common Factor And Lowest Common Multiple

Read And Learn More: WBBSE Notes For Class 6 Maths Chapter 1 Simplification

WBBSE Class 6 HCF and LCM Notes

Chapter 1 Lowest Common Multiple

A number has an infinite number of multiples.

Two numbers may have infinite numbers of common multiples.

Lowest Common Multiple Definition

  1. The lowest of all the common multiples of two numbers is called the L. C. M. or the Lowest Common Multiple of the numbers.
  2. For example, we consider the numbers 15 and 25.
  3. The multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ………
  4. The multiples of 25 are 25, 50, 75, 100, 125, 150,……..
  5. Among these multiples, the common multiples are 75, 150,…………..
  6. ∴ The lowest common multiple is 75.
  7. So the required L. C. M. of 15 and 25 = 75.
  8. The L. C. M. of two given numbers can be determined in two processes as follows:
    1. Resolution into prime factors
    2. Division method.
  9. In the illustrative examples discussed below, both processes are described to determine the L. C. M. of two numbers.

Understanding HCF and LCM

Formula:

The product of two numbers H. C. F. x L. C. M. of two number

Leave a Comment