Question

please solve this....
find the natural number in ratio 5:7 such that their l.c.m is 210

Answer 1

Let the numbers be 5x and 7x.

LCM of 5x and 7x = 35x

Given that LCM of 5x and 7x = 210.

35x = 210

x = 6.


Hence the 1st number = 5x

                                       = 5 * 6

                                       = 30.


Hence the 2nd number = 7x

                                         = 7*6

                                         = 42.


Therefore the natural numbers are 30 and 42.


Hop this helps!

Answer 2

l.c.m = 210
ratio of numbers: 5 : 7
H.C.F * L.C.M = product of numbers......(i)
If the numbers are 5X , 7X: then HCF is 'X'.
Applying this in (i)

X * 210 = 5X * 7X
210X = 35X^2
210 = 35*X
X = 6

Our numbers were 5X , 7X
Hence: 5*6 = 30, 7*6 = 42
Hence numbers are: 30 , 42.
Hope it helps