Ray's New Higher Arithmetic · Arts. 101–104 · Unit 7: Properties of Numbers
27. The least common multiple
Goal: Your student finds the least common multiple of several numbers by factoring them and by dividing them together by common primes.
You'll need
- The book
- A slate, small whiteboard or scrap paper
- A notebook and pencil
What's in the book
Common multiple and least common multiple defined, six principles, Case I by factoring each number, Case II by dividing by common primes (with the rule for striking out numbers that divide others), and two sets of examples with printed answers.
The lesson, step by step
Warm-up
Mental: What is the smallest number that both 4 and 6 divide? (12.)
The idea
Read:
the least number that is divisible by each of them without a remainder.
and the principle for numbers with no common factor:
their continued product is their least common multiple.
Case I
Read:
Resolve each number into its prime factors, and then take the continued product of all the different prime factors.
Take each factor as many times as it appears in any one number. The book's example 10, 12, 15: 2 × 2 × 3 × 5 = 60.
Case II
Read:
Write the numbers in a horizontal line; strike out any number that will exactly divide any of the others
Divide the rest by a prime that goes into two or more, bring down the others, and repeat. Then:
their product will be the least common multiple required
Work the book's example 10, 20, 25, 30: strike out 10; answer 300.
Guided practice
Together:
1. 8, 10, 15. Ans. 120.
1. 6, 9, 20. Ans. 180.
Independent practice
Your student works both sets of examples (6 under Case I, 10 under Case II).
Wrap-up
Ask: Where will you need the L. C. M. soon? (Adding fractions: the least common denominator.)