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Content
Content
- Highest Common Factor
- Finding Highest Common Factor
- Lowest Common Multiple
- Finding Lowest Common Multiple
- Squares, Cubes
- Square Root, Cubic Root
HCF - Highest Common Factor
HCF - Highest Common Factor
Factors of 4 are 1, 2, 4.
Factors of 16 are 1, 2, 4, 8, 16.
Common factors of 4 and 16 are 1, 2, 4.
Highest Common Factor (HCF) of 4 and 16 is 4.
Finding Highest Common Factor
Finding Highest Common Factor
The highest common factor (HCF) of two or more numbers is the largest number which can divide all of them.
Divide both numbers by 2,3,5,7,11…(prime numbers), starting with 2 first.
Stop when you cannot divide both numbers.
Multiply the dividends to get HCF.
HCF = 2 x 3 = 6
LCM - Lowest Common Multiple
LCM - Lowest Common Multiple
Multiples of 3 are 3, 6, 9, 12, 15, ...
Multiples of 4 are 4, 8, 12, 16, 20....
Lowest Common Multiple of 3 and 4 is 12.
Finding lowest common multiple
Finding lowest common multiple
The lowest common multiple (LCM) of two or more numbers is the smallest number that all of them can divide.
Divide both numbers by 2,3,5,7,11…(prime numbers) starting with 2 first.
When you cannot divide both numbers, divide one number at a time.
Stop when you get all 1’s.
Multiply the dividends.
LCM = 2 x 3 X 2 X 3 = 36.
Squares
Squares
22 = 2 x 2 = 4
82 = 8 x 8 = 64
Cubes
Cubes
23 = 2 x 2 x 2 = 8
83 = 8 x 8 x 8 = 512
Square Root
Square Root
To find the square root of 144
√144 = √ (2 x 2 x 2 x 2 x 3 x 3) (by Prime Factorisation)
= 2 x 2 x 3 ( take one number for every pair)
= 12
Cubic Root
Cubic Root
To find the cubic root of 64
∛(64) = ∛ (2 x 2 x 2 x 2 x 2 x 2) (by Prime Factorisation)
= 2 x 2 ( take one number for every three numbers )
= 4
Questions
Questions
- Find the shortest length of a wire that can be cut into pieces of either 4 cm or 6 cm or 9 cm without any leftover.
- James and Kelly run started jogging around a track at the same time. James takes 4 minutes to complete a round while Kelly takes 3 minutes to complete a round. How long (in seconds) it will take for both of them to be at the starting point again?
- Muthu wants to cut a gift paper measuring 60 cm by 48 cm into largest possible squares without any wastage. What is the length of each square? How many such squares can be cut from the gift paper?
- Three buses A,B,C leave an interchange at 6:00 am. Bus A makes a trip every 15 minutes, Bus B makes a trip every 20 minutes and Bus C makes a trip every 25 minutes. At what time all three buses will be at the interchange again?
- 525 pens, 315 pencils were shared equally among a group of children. Find the smallest and largest possible number of children in the group.
- Find the smallest integer n such that 24n is a perfect square.
- Find the smallest integer m such that 54m is a perfect cube.
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