Question

Three number are in the ratio of 3 : 4 : 5 and their l.c.m. is 1200. their h.c.f. is:

Answer 1

Thanks for the question!

It is definitely a very interesting question to solve and do some brainstorming.

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Let the numbers be 3x, 4x and 5x.

 Then, their L.C.M. = 60x.

 So, 60x = 1200 or x = 20.

 

 The numbers are (3 x 20), (4 x 20) and (5 x 20) i.e. 60, 80, 100

 Hence, required H.C.F. = 20.

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Hope it helps and solves your query!!

Answer 2

The Numbers are in the Ration 3 : 4 : 5,

Let the numbers be 3x , 4x , 5x

x is common in all the numbers,
so,
=>  L.C.M. = x × 3×4×5
=>  1200 = 60x
=>   x= 20

Now, again, x is common factors in all the numbers,
So, X is the H.C.F. is x= 20


So the H.C.F. of the number is 20