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The Relation Between G.C.D and L.C.M:

For GCD concept click here:http://business-maths.blogspot.com/2009/02/greatest-common-divisor.html
For LCM concept click here:http://business-maths.blogspot.com/2009/02/least-common-multiple-lcm.html
Find the G.C.D and L.C.M of 30 and 48 and it shows that the product of GCD and LCM is equal to the product of the two given numbers.
GCD of 30,48 is 6.
And LCM of 30,40 is 240.
LCM*GCD=240*6=1440
Product of 30 and 48= 30*48=1440.
Hence the product of the two numbers is equal to the product of their G.C.D and L.C.M.
If a and b are any two natural numbers and L and G are respectively their L.C.M and G.C.D., then a*b=L*G

->(a+b)²=a²+b²+2ab
->(a-b)²=a²+b²-2ab
->(a+b)²-(a-b)²=4ab
->(a+b)²+(a-b)²=2(a²+b²)
->a²-b²=(a+b)(a-b)
->(a-+b+c)²=a²+b²+c²+2(ab+b c+ca)
->a³+b³=(a+b)(a²+b²-ab)
->a³-b³=(a-b)(a²+b²+ab)
->a³+b³+c³-3a b c=(a+b+c)(a²+b²+c²-ab-b c-ca)
->If a+b+c=0 then a³+b³+c³=3a b c