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Permutations And Combinations

Question

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Find L.C.M. and H.C.F. of 2 x 2!, 4! and 3 x 5!

Solution

2 cross times 2 factorial space equals space 2 cross times 2 cross times 1 space equals space 2 squared space space space

space space space 4 factorial space equals space 4 cross times 3 cross times 2 cross times 1 space equals space 2 cubed cross times 3 to the power of 1

3 cross times 5 factorial space equals space 3 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 space equals space 2 cubed cross times 3 squared cross times 5 to the power of 1

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L.C.M. =

space space space 2 cubed cross times 3 squared cross times 5 to the power of 1 equals 2 cross times 2 cross times 2 cross times 3 cross times 3 cross times 5

= (5 x 4 x 3 x 2 x 1) x 3 = 3 x 5!
and H.C.F. = 2² = 2 x (2 x 1) = 2 x 2!

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