Question

# Three number are in the ratio of $$3 : 4 : 5$$ and their L.C.M. is $$2400$$. Their H.C.F. is:

A
40
B
80
C
120
D
200

Solution

## The correct option is A $$40$$Let the numbers be $$3x$$, $$4x$$ and $$5x$$.Then, their L.C.M. $$= 60x$$.So, $$60x = 2400$$ or $$x = 40$$.$$\therefore$$ The numbers are $$\left( 3\times 40 \right)$$, $$\left( 4\times 40 \right)$$ and $$\left( 5\times 40 \right)$$.Hence, required H.C.F. $$= 40$$.Maths

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