Given:
The G.C.F of 2 numbers is 36.
The product of the 2 numbers is 23328.
To find:
The L.C.M. of the 2 numbers.
Solution:
If a and b are two numbers, then
[tex]L.C.M.(a,b)\times H.C.F.(a,b)=a\times b[/tex] ...(i)
We know that H.C.F. is equal to G.C.F.
Putting H.C.F. (a,b)= 36 and [tex]a\times b=23328[/tex] in (i), we get
[tex]L.C.M.(a,b)\times 36=23328[/tex]
Divide both sides by 36.
[tex]L.C.M.(a,b)=\dfrac{23328}{36}[/tex]
[tex]L.C.M.(a,b)=648[/tex]
Therefore, the L.C.M. of the 2 numbers is 648.
