GREATEST COMMON FACTOR&LEAST COMMON MULTIPLE : GREATEST COMMON FACTOR&LEAST COMMON MULTIPLE BY:
Monali Thakur
monali_253@yahoo.co.in
Slide 2 : The greatest common factor of two or more whole numbers
is the largest whole number that divides evenly into
each of the numbers Definition of GCF
Slide 3 : What is a "Factor" ?
Factors are the numbers you multiply together to get another number: Sometimes we want to find ALL the factors of a number:
The factors of 12 are 1,2,3,4,6 and 12 ...... because 2 × 6 = 12, or 4 × 3 = 12, or 1 × 12 = 12.
Slide 4 : What is a "Common Factor" ?
Let us say you have worked out the factors of two or more numbers:
Example: Then the common factors are those that are found in both numbers:
Notice that 1,2,3 and 6 appear in both lists?
So, the common factors of 12 and 30 are: 1, 2, 3 and 6
It is a common factor when it is a factor of two or more numbers.(It is then "common to" those numbers.)
Slide 5 : The first method is to list all of the factors of each number,
then list the common factors and choose the largest one.
Example: Find the GCF of 36 and 54.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
The common factors of 36 and 54 are 1, 2, 3, 6, 9, 18
Although the numbers in bold are all common factors of both 36 and 54,
18 is the greatest common factor.
Slide 6 : Example: And another example:
Slide 7 : The second method is to list the prime factors,
then multiply the common prime factors.
Example: Let's use the same numbers, 36 and 54.
The prime factorization of 36 is 2 x 2 x 3 x 3
The prime factorization of 54 is 2 x 3 x 3 x 3
Notice that the prime factorizations of 36 and 54
both have one 2 and two 3s in common.
So, we simply multiply these common prime factors
to find the greatest common factor
. Like this...
2 x 3 x 3 = 18
Both methods work!
Slide 8 :
Slide 9 : Definition of LCM The least common multiple of two or more non-zero whole numbers
is actually the smallest whole number that is divisible by each of the numbers.
Slide 10 : Simply list the multiples of each number (multiply by 2, 3, 4, etc.)
then look for the smallest number that appears in each list.
Example: Find the least common multiple for 5, 6, and 15.
First we list the multiples of each number.
Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,...
Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,...
Multiples of 15 are 30, 45, 60, 75, 90,....
Now, when you look at the list of multiples,
you can see that 30 is the smallest number that appears in each list.
Therefore, the least common multiple of 5, 6 and 15 is 30.
Slide 11 : We can find the LCM by using a quicker method of prime factorising the number.
e.g.
Find the LCM of 15,25,30.
15 25 30 3
5 5 25 10 1 5 2 The product of the common factors and the remaining numbers is the LCM.
LCM of 15,25,30 is
= 3 x 5 x 5 x 2
= 150
Slide 12 : LET US SOLVE SOME EXAMPLES ON GCF AND LCM
Slide 13 : Find the GCF of 36,45,72
Slide 14 : Find the HCF of 300,396
Slide 15 : Find the HCF of 1356,226
Slide 16 : Find the LCM of 192, 216,120
Slide 17 : Find the LCM of 105,135,150
Slide 18 : Find the LCM of 112,144,160
Slide 19 : The product of the HCF and the LCM of any two numbers is always equal to the product of the given numbers HCF X LCM = Product of the two numbers
Slide 20 : any doubts??
Slide 21 : THANK YOU!!