Search for notes by fellow students, in your own course and all over the country.
Browse our notes for titles which look like what you need, you can preview any of the notes via a sample of the contents. After you're happy these are the notes you're after simply pop them into your shopping cart.
Title: Algebra _ Least Common Multiple (L.C.M.)
Description: Algebra _ Least Common Multiple (L.C.M.) The Least Common Multiple ( LCM ) is also referred to as the Lowest Common Multiple ( LCM ) and Least Common Divisor ( LCD) . For two integers a and b, den oted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b.
Description: Algebra _ Least Common Multiple (L.C.M.) The Least Common Multiple ( LCM ) is also referred to as the Lowest Common Multiple ( LCM ) and Least Common Divisor ( LCD) . For two integers a and b, den oted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b.
Document Preview
Extracts from the notes are below, to see the PDF you'll receive please use the links above
Algebra
Least Common Multiple (L
...
M
...
L
...
M by Factorization
Find the L
...
M of the following:
(i)
3 a4 b2 c3, 5 a2 b3 c5
Solution:
L
...
M of 3 x 5 =15
L
...
M of 3 a4 b2 c3 , 5 a2 b3 c5 is 15 a4 b3 c5
(ii)
15 x3 y3 z, 25 x y3 z2
Solution:
5
15, 25
3, 5
L
...
M of 15 x3 y3 z, 25 x y3 z2 is 75 x3 y3 z2
(iii)
15 p3 q4, 20 m2 p2 q3, 30 m p3
Solution:
5
15, 20, 30
2
3,
4,
6
3
3,
2,
3
1,
2,
1
L
...
M of 15 p3 q4, 20 m2 p2 q3 , 30 m p3 is 60 p3 q4 m2
...
Find the L
...
M of the following:
(i)
x2 – 1, ( x – 1)2
Solution:
x2 – 1
= ( x + 1) ( x –1)
2
(ii)
( x – 1)
= ( x – 1)2
L
...
M
= ( x – 1)2 ( x + 1)
x3 – y3, x2 – y2
Solution:
x3 – y3
= ( x y) ( x2 + xy + y2)
( x2 – y2)
= ( x + y) ( x – y)
L
...
M
= ( x – y ) ( x + y) ( x2 + xy +y2)
=
(iii)
( x + y) ( x3 – y3)
x2 – 10x + 24, x2 – 11x + 30
Solution:
x2 – 10x + 24 = ( x – 4) ( x – 6)
x2 – 11x + 30 = ( x – 5) ( x – 6)
L
...
M = ( x – 4) ( x 5 ) ( x – 6)
(iv)
13 ( x – 1) ( x – 2)2, 7(x – 2)2 ( x + 3)2, ( x – 1)2 ( x + 3)
Solution:
L
...
M
= 91( x – 1)2 ( x – 2) 2( x + 3) 2
(v)
x2 – 12x + 35, x2 – 8x + 7, x3 – 5x2 – x + 5
Solution:
x2 – 12x + 35 = (x – 5) (x – 7)
x2 – 8x + 7
x3 – 5x2 – x+ 5
= (x – 7) (x – 1)
= x2 (x – 5) –1 (x – 5)
= (x – 5) (x2 – 1)
= (x – 5) (x + 1) (x – 1)
L
...
M = (x – 5) (x – 7) (x – 1) (x + 1)
(vi)
6x2 – x – 1 , 3x2 + 7x + 2, 2x2 + 3x – 2
Solution:
6x2 – x – 1 = (2x –1) (3x + 1)
3x2 + 7x + 2 = (3x + 1) (x + 2)
2x2 + 3x – 2 = (2x – 1) (x + 2)
L
...
M = (2x – 1) (3x + 1) (x + 2)
(vii)
x3 + x2 + x + 1, x3 + 2x2 + x + 2
Solution:
x3 + x2 + x + 1 = x2 (x + 1) + 1 (x + 1) = (x + 1) ( x2 + 1)
x3 + 2x2 + x + 2 = x2 (x + 2) + 1 (x + 2) = (x + 2) ( x2 + 1)
L
...
M = (x + 1) (x + 2) (x2 + 1)
Title: Algebra _ Least Common Multiple (L.C.M.)
Description: Algebra _ Least Common Multiple (L.C.M.) The Least Common Multiple ( LCM ) is also referred to as the Lowest Common Multiple ( LCM ) and Least Common Divisor ( LCD) . For two integers a and b, den oted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b.
Description: Algebra _ Least Common Multiple (L.C.M.) The Least Common Multiple ( LCM ) is also referred to as the Lowest Common Multiple ( LCM ) and Least Common Divisor ( LCD) . For two integers a and b, den oted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b.