Becky Afghani, LBUSD Math Curriculum Office, 2003 Snack Problem! Cookout Problem! Serena wants to create snack bags for a trip she is going on. She has 6 granola and 10 pieces of fruit. If the snack bags should be identical without any food left over, what is the greatest amount of snack bags Serena can make? Hot dogs come in packages of 8. Hot dog buns come in packages of 12. Grace wants to have an equal amount of buns and hot dogs so that every bun has a hot dog. What is the least amount of packs of each that will she need to buy so she has no buns or hot dogs left over? How are the two problems similar? How are the two problems different? Becky Afghani, LBUSD Math Curriculum Office, 2003

The Listing Method For Finding LCM MCC6.NS.4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.

What are multiples? Multiples are defined as the product of a number and any whole number. 6x0=0 6x6=36 6x1=6 6x7=42 6x2=12 6x8=48 16x0=0 6 6x3=18 16x1=16 16 6x4=24 16x2=32 6x5=30 16x3=48 Becky Afghani, LBUSD Math Curriculum Office, 2003

What is meant by smallest common multiple or LCM? The LCM is the smallest multiple that two or more numbers have in common. 6x0=0 6x6=36 6x1=6 6x7=42 6 6x2=12 6x8=48 16x0=0 6x3=18 16x1=16 16 6x4=24 16x2=32 6x5=30 The LCM of 6 and 16 is 48. 16x3=48 Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003 Cookout Problem! Hot dogs come in packages of 8. Hot dog buns come in packages of 12. Grace wants to have an equal amount of buns and hot dogs so that every bun has a hot dog. What is the least amount of packs of each that will she need to buy so she has no buns or hot dogs left over? Becky Afghani, LBUSD Math Curriculum Office, 2003

The Ladder Method For Finding LCM

Let’s find the Least Common Multiple (LCM) of 28 and 70 The LCM is the product of all the numbers on the left and the bottom. The LCM of 28 and 70 is 140. 2 28 70 7 14 35 2 5 2x7x2x5 = 140 Becky Afghani, LBUSD Math Curriculum Office, 2003

Which numbers in the ladder give you the LCM? The “L” shape gives you the LCM: multiply the numbers on the left and bottom. # # # # # # # # # # # Becky Afghani, LBUSD Math Curriculum Office, 2003

Let’s try some bigger numbers. Divide out all the common factors down the left side. 2 24 60 What number goes into both 24 and 60? Does any # besides 1 go into both 12 and 30? 2 12 30 How about 6 and 15? Anything else? 3 6 15 No? You’re done. 2 5 Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003 Find the LCM. x The LCM of 24 and 60 is 120. 24 60 2 12 30 6 15 3 5 = 120 Becky Afghani, LBUSD Math Curriculum Office, 2003

Becky Afghani, LBUSD Math Curriculum Office, 2003 Find the GCF. x The GCF of 24 and 60 is 12. 24 60 2 12 30 6 15 3 5 = 12 Becky Afghani, LBUSD Math Curriculum Office, 2003

Practice. Find the LCM for 28 and 42. 7 14 21 2 3 Becky Afghani, LBUSD Math Curriculum Office, 2003

Practice. Find the GCF for 28 and 42. 7 14 21 2 3 Becky Afghani, LBUSD Math Curriculum Office, 2003