Notes of Lessons: Arithmetic, Class II

Notes of Lessons: Arithmetic, Class II

[We have thought that it might be of use to our readers (in their own families) to publish from month to month during the current year, Notes of Lessons prepared by students of the House of Education for the pupils of the Practising School. We should like to say, however, that such a Lesson is never given as a tour de force, but is always an illustration or an expansion of some part of the children’s regular studies (in the Parents’ Review School), some passage in one or other of their school books.—Ed.]

Group: Mathematics • Class II • Time: 20 minutes

By Marion Rothera
The Parents’ Review, 1904, pp. 468-469


I. To introduce least common multiples to P_____ and H_____.

II. To connect the lesson with greatest common measures, which the children have just finished.

III. To increase the children’s power of rapid mental work.


Step I.—Draw from the children the difference between a “measure” and a “multiple” of a number. Let them give examples, as, 4 is a measure of 8, 16, 20, etc., and 8, 16 are multiples of 4.

Step II.—Ask the children what numbers are multiples of both 2 and 3; as 6, 12, 18. Point out that these are common multiples. Give them other examples of common multiples. Then draw from them what the least common multiple of 2 and 3 is. Give other examples to be worked mentally.

Step III.—Draw from the children the definition of the “least common multiple” of two numbers, and write it on the board, viz.:

The least common multiple of two numbers is the least number into which each of the numbers will divide without a remainder.

Step IV.—Find the L. C. M. of 4 and 10. Work this on the board thus:—

4 = 2 x 2

10 = 2 x 5   ∴   L. C. M. = 2 x 2 x 5 = 20

i.e., the G. C. M. of the two numbers multiplied by all the other prime factors.

Step V.—Give the children similar exercises that they can work mentally, as:—

Find the L. C. M. of 6 and 14, 4 and 6, 6 and 15, etc.

Step VI.—Give the children harder exercises and let them work them on the board in turn, as:—

Find the L. C. M. of 72 and 108, 24 and 88, etc.