Question

Three numbers are in the ratio $3:4:5$, and their LCM is $2400$; then its HCF is ___?

Answer 1

Let us consider the number be $3x,4xand5x$

$TheL.C.Mofthethreenumbersbe=60x$

$60x=2400$

$x=2400/60$

$x=40$

Then the number be:

$3x=3\times 40=120$

$4x=4\times 40=160$

$5x=5\times 40=200$
Since $40$ is common.

∴ Hence the HCF of the three numbers be$40$.