Question

two numbers are in ratio of 5:7 and their LCM is 420 .what is the difference between two numbers????????

Answer 1

Let the numbers be 5x and 7x , as they are in ration of 5:7.

LCM = Least Common Multiple.

HCF = Highest Common factor.

Then, LCM = 420 (Given.)

∴ HCF = x (Highest common factor, we can see = x.)

We know that,  

Product of numbers = LCM × HCF

∴ 5x × 7x = 420 × x

∴ $\bold{35x^{2} = 420x}$

∴ $\bold{x^{2} and\:x\:cancel\:each\:other}$

∴ $\bold{35x = 420}$

∴ $\bold{x = \frac{420}{35}}$

∴ $\bold{x\:=\:12}$

The numbers we assumed were 5x and 7x

∴ $\bold{5x\:=\:12\times5\:\implies60}$

∴ $\bold{7x\:=\:12\times7\:\implies84}$

∴ Numbers are 60 and 84 respectively.

Thanks!

Answer 2

Given LCM or Least Common Multiple of two number is =420

The ration of two number is 5:7

Let consider the two number are 5x and 7x

The HCF or Highest Common factor of of 5x and 7x is x

We know that

The product of two number = product of their HCF and LCM

$5x\times7x=420\times{x}\\\\\Rightarrow35x=420\\\\\Rightarrow{x}=\frac{420}{35}\\\\\Rightarrow{x}=12$

Therefore the two numbers are $5x=5\times12=60$ and $7x=7\times12=84$

The difference between these two number is = (84-60)=24