GCF and LCM Lesson

GCF and LCM Lesson

by Mr. Nakagama

​Finding Greatest Common Factor (GCF)

​-Make factor trees of both numbers: Split off as you work your way down finding primes(think 2,3,5,7,9,11)

​

​-Find common factors and multiply: Find the common prime factors that are present in both numbers. DOn't miss multiples of them. Then multiply those primes.

​-That's it... you've found the GCF

​Finding the Least Common Multiple (LCM)

​-Make a factor tree: Same as with GCF, make a factor tree of primes. I like to split to the right.

​- Find greatest occurrence of each distinct prime numbers. Multiply them

​- Notice we used both two's... we needed greatest occurrence.

​When do we use GCF and LCM

​LCM

​Used to find common denominators

​---Word Problem Signal Phrases---

​

​Repetition

​cycles/patterns

​two things - happening at the same time

​smallest or least number of sets

​GCF

Used to reduce/simplify fractions

​​---Word Problem Signal Phrases---

​groups or sets no remainder

​splitting/dividing equally

​Share

​No Leftovers

​Greatest or Largest

Multiple Choice

What should we use?

At the gym, Hillary swims every 6 days, runs every 4 days, and cycles every 16 days. If she did all three activities today, in how many days will she do all three activities again on the same day?

• GCF

• LCM

LCM​

Because we are looking for two or more things happening at the same time. ​

Multiple Choice

Which should we use?

Oscar needs to ship 14 rock CDs, 12 classical CDs, and 8 pop CDs. He can pack only one type of CD in each box, and he must pack the same number of CDs in each box. What is the greatest number of CDs Oscar can pack in each box?

• LCM

• GCF

Greatest Common Factor​

​The question had greatest in it and it asked us to divide something

Multiple Choice

At the gym, Hillary swims every 6 days, runs every 4 days, and cycles every 16 days. If she did all three activities today, in how many days will she do all three activities again on the same day?

• 2

• 12

• 16

• 48

Fill in the Blanks

I want to plant 45 sunflower plants, 81 corn plants and 63 tomato plants in my garden. If I put the same number of plants in each row and each row has only one type of plant, what is the greatest number of plants I can put in one row?

Only input the number; no spaces and no words.

​LCM's and GCF's

​Hopefully after this quick refresher you are now ready to tackle any word problem that uses one of these two strategies.