USING FACTORS and MULTIPLES in REAL LIFE GCF
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USING FACTORS and MULTIPLES in REAL LIFE GCF and LCM August 24, 2015 Mrs. Holder
GCF (Greatest Common Factor) largest factor GCF is the two or more numbers have in common. EXAMPLE: Find the GCF of 15, 30 and 105 • Notice that the GCF can be EQUAL or SMALLER than the lowest number in the set being compared. Factors of 15 are: 1, 3, 5, 15 Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30 Factors of 105 are: 1, 3, 5, 7, 15, 21, 35, 105 ALL NUMBERS have a factor 1! It’s a very special number (neither PRIME, nor Composite!
LCM (Least Common Multiple) LCM is the LOWEST MULTIPLE greater than 0 that two or more numbers have in common. EXAMPLE: Find the LCM of 6, 8 and 12. Multiples of 6: 6, 12, 18, 24, 30, 36 Multiples of 8: 8, 16, 24, 32 Multiples of 12: 12, 24, 36 • Notice that the LCM is LARGER than the numbers being compared. • LCM can be equal or larger than the BIGGEST number in the set you are comparing.
A Game of Kickball Mrs. Holder, Mrs. Moss and Mrs. Lumsden are planning an after-school competitive game of kickball for their students as an award. Classes need to be split into the same number of teams. 42 students in Mrs. Holder’s class came to the game. 48 students in Mrs. Lumsden’s class came to the game. 54 students in Mrs. Moss’ class came to the game What is the How many students will be on each team? greatest number of teams the classess can be split into?
Another Method to find GCF SLED METHOD: List the numbers you are comparing in a row. 2 42 48 54 3 21 24 7 8 27 9 • MULTIPLY COMMON FACTORS: • 2 x 3=6 • 6 is the greatest number of teams each class can have. • Use upside down division to break out common factors (try to use prime factors). • Continue to divide by a common factor until the numbers do not have any factors in common. • Multiply ONLY common factors together to get GCF.
Hot Dogs and Hot Dog Buns What is George’s Problem? What could he have done to solve it?
SOLVING THE HOT DOG BUN DILEMMA with the SLED Method Find LCM – because we need to have the same number of hot dogs and buns in order not to waste any. 2 8 2 4 2 12 6 3 Divide by a common prime factor. Multiply Common and Uncommon Factors to get LCM> 2 x 2 x 3 = 24 Need to buy 24 hotdogs (3 packages) and 24 buns (2 packages) in order to not have extra buns!
How do I know when to use GCF and LCM USE GCF when the problem has…. Splitting things into smaller groups Trying to find out how many people we can invite Arranging something into rows or groups Ø Use LCM when the problem has…. Ø Is there an event that is repeating over and over? Ø Do we need to purchase multiple packages of something to have enough or the same number? Ø Are we trying to find when something will happen again at the same time?
