Question

The LCM of two numbers is 28 times of their HCF the sum of their LCM and HCF is 1740 one number is 240 find other

Answer 1

lcm=hcf×28

=lcm:hcf=28:1

=lcm=28x

=hcf=x

Now

lcm+hcf=1740

=28x+x=1740

29x=1740x=60

=lcm=28x=28×60

=hcf=x=60

=first number=240

second number =lcm×hcf/first number

= 28×60×60/240

=7×60=420

u r ans

Answer 2

$\bold{\underline{\underline{Assume\::}}}$

Let the -

• other number be "M"

$\bold{\underline{\underline{Solution\::}}}$

Given :

• LCM is 28 times HCF
• Sum of LCM and HCF is 1740
• One number is 240.

Find :

Other number.

According to question,

⇒ LCM = 28 × HCF ____ (eq 1)

Also,

⇒ LCM + HCF = 1740

⇒ 28HCF + HCF = 1740 [From (eq 1)]

⇒ 29HCF = 1740

⇒ HCF = 60

Substitute value of HCF in (eq 1)

⇒ LCM = 28 × 60

⇒ LCM = 1680

Now,

Product of two numbers = LCM × HCF

Product of two numbers = one number × other number

Substitute the known values in above formula

⇒ 240 × M = 1680 × 60

⇒ M = (1680 × 60)240

⇒ M = 7 × 60

⇒ M = 420

∴ Other number is 420.