Ray's New Practical Arithmetic · Art. 90 · Unit 9: Factoring
50. Least common multiple
Goal: Your child finds the least common multiple of several numbers by short division.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
The principle of the L. C. M., a worked example (4, 6, 9 and 12), the rule by short division, and problems 2 to 23 with printed answers.
The lesson, step by step
Warm-up
Count by 4s and by 6s aloud. Where do they first meet? (12.)
The principle
Read:
The L. C. M. of two or more numbers contains all the prime factors of each number and no other factor.
Work the book example
Find the L. C. M. of 4, 6, 9 and 12. Divide by 2: 2, 3, 9, 6. By 2 again: 1, 3, 9, 3. By 3: 1, 1, 3, 1. Multiply the divisors and what's left: 2 × 2 × 3 × 3 = 36.
The rule
Read:
Divide by any prime number that will exactly divide two or more of them.
Write the quotients and undivided numbers in a line beneath.
Then read the last step from the rule on the page.
Guided practice
Together:
2, 3, 4, 5, 6, 7, 8 and 9.
(2520, the smallest number all of them divide.)
Independent practice
Your child does problems 2 to 19.
Check and wrap-up
Answers are printed. Mental: L. C. M. of 3 and 4? Of 6 and 8? Of 10 and 15?