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Multiples and Least Common Multiples
Section 5.2 B
Here is a video of the “ladder” or “L” algorithm for finding the least common multiple: Watch it, please.
What is a multiple of a number? When we have two or more numbers we can find the multiples they
have in common, and often we want the smallest of these.
Again your book uses the Set Intersection Method. Describe this method? ________________________
The “L” algorithm is a prime factorization method that keeps the numbers organized.
Here is how we would find the LCM of 24 and 36 using the “L” algorithm:
Step 1: Write the two numbers
Step 2: On the right, write a common prime:
Step 3: Divide and write a second common prime factor:
Step 4: Stop when no common prime factor is left:
24 36
24 36
2) 24 36
2) 24 36
2) 12 18 see the L? 2) 12 18
3) 6 9
3) 6 9
2 3
2 3
Step 5: Multiply the primes that were divided out with the remaining primes at the bottom of the L.
This is your least common multiple: 22 x 3 x 2 x 3 = 144
WAIT A MINUTE!!! Didn’t we just use this algorithm to find the GCF???
The advantage of the L algorithm is that students find both the GCF and the LCM at the same time.
Practice using the L algorithm on the A problems in your book, and then write an explanation for the
theorem at the bottom of page 220. The class will be relying upon your work to help us put together a
final explanation. One student noticed that the LCM and the GCF can be found when we use a Venn
diagram to sort the prime factors of two numbers:
Let A = Factors of 24
Let B = Factors of 36
What SET is GCF(24, 36) ?
What SET is LCM(24, 36) ?
Homework due Monday, January 14:
5.2B #7
5.2B #10
5.2B #24
5.2B #25
Ignore the directions, use the algorithm taught in class only
Do not use a factor tree, use our new algorithm
Make sure you PROVE this!