Math, asked by animeshbhardwaj61, 5 months ago


The LCM of two numbers is 28 times of their
HCF. The sum of their LCM and HCF is 1740. If
one number is 240 then what is the other
number?
(b) 460 (c) 500
(d) 380
(a) 420​

Answers

Answered by tannu5714
24

Answer:

(a) 420

Step-by-step explanation:

let the hcf is x

so lcm will be 28x

lcm+hcf=1740

28x+x=1740

29x=1740

x=1740÷29

x=60

so hcf is 60

and lcm =60×28=1680

now hcf×lcm=product of the nmbers

so 1680×60=240×2nd number

100800÷240=2nd number

420=2nd number

Answered by ShírIey
91

Given:

  • The LCM of two numbers is 28 times of their HCF.

:\implies\sf LCM = 28 HCF

Also,

  • The sum of their LCM and HCF is 1740.

:\implies\sf LCM + HCF = 1740

Now,

:\implies\sf 28HCF + HCF = 1740 \\\\\\:\implies\sf 29 HCF = 1740 \\\\\\:\implies\sf  HCF = \cancel\dfrac{1740}{29}\\\\\\:\implies{\underline{\boxed{\sf{HCF = 60}}}}

As, LCM = 28 HCF.

Therefore,

:\implies\sf LCM = 28 \times 60\\\\\\:\implies{\underline{\boxed{\sf{LCM =  1680}}}}

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

Finding the other number,

  • One number is equal to 240.

Hence,

:\implies\sf Number = \bigg(\dfrac{HCF \times LCM}{One \; number}\bigg)\\\\\\:\implies\sf  Number =  \bigg(\dfrac{60 \times 1680}{240} \bigg)\\\\\\:\implies\sf Number = \cancel\dfrac{100800}{240}\\\\\\:\implies{\underline{\boxed{\sf{\pink{ Number = 420}}}}}\:\bigstar

\therefore{\underline{\sf{Hence,\: other\; required\; number\;is\; \bf{Option\;a)\:420 }.}}}

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