Math 6 NOTES: 1.4a (Unit 1, Lesson 4a)
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Least Common Multiple (LCM) - 1.4a NOTES
TERM
Multiple
DEFINITION
EXAMPLE
Least Common
Multiple (LCM)
Find the LCM…
Method #1 – List the multiples of each number.
Multiples of 6:
Multiples of 10:
Write the multiples of each number.
Start with the greater number.
Stop when you find a common
multiple!
What is the least common multiple?
TRY IT!
1)
Find the LCM of 3 and 12. (Remember to start with the greater number).
3:
12:
2)
Find the LCM of 4 and 5.
4:
5:
Method #2 – Find the LCM Using Prime Factors
Find the LCM of 24 and 36.
Step 1: Find the prime factorization of 24 and 36.
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Step 2: Circle all prime factors and write the prime factorization of each number
(Remember to put them in order from least to greatest!)
24: 2 · 2 · 2 · 3
36: 2 · 2 · 3 · 3
Step 3: Write repeating prime factors as an exponent, then circle the greatest power.
24: 23 · 3
23 · 3
36: 22 · 32
22 · 32
Exponents show repeated
multiplication.
Step 4: Multiply the greatest power of each of the prime factors to obtain LCM.
23 · 32
2 · 2 · 2 · 3 · 3 = 72
Try It!
1)
Find the LCM of 10, 20, and 30.
2)
Find the LCM of 16, 32, and 64.
3)
Find the LCM of 6, 17, and 34.