Question 28

Three numbers in the ratio 3 : 4 : 5 have the LCM 2400. What is the HCF?

Solution

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

their L.C.M. = 60x.

So, 60x = 2400 or x = 40.

The numbers are (3 x 40), (4 x 40) and (5 x 40).

HCF

120 = $$2\times 2\times 2\times 3\times 5$$

160 = $$2\times 2\times 2\times 2\times 2\times 5$$

200 = $$2\times 2\times 2\times 5\times 5$$

H.C.F. = 40.

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