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

1.	The LCM of two numbers is 28 times of their HCF. The sum of their LCM and HCF is 1740. If one of the numbers is 240, find the other number. (a) 240 (b) 620 (c) 540 (d) 420
Answer» Answer is (d) 420 LCM = 28 HCF Also, LCM + HCF = 1740 ⇒ 28 HCF + HCF = 1740 ⇒ 29 HCF = 1740 ⇒ HCF = \(\frac{1740}{29}=60\) ⇒ LCM = 28 × 60 = 1680 Since, one number = 240 ∴ Other number = \(\frac{HCF \times LCM}{One\,number}\) = \(\frac{60 \times 1680}{240}\) = 420

The LCM of two numbers is 28 times of their HCF. The sum of their LCM and HCF is 1740. If one of the numbers is 240, find the other number. (a) 240 (b) 620 (c) 540 (d) 420

Answer»

Answer is (d) 420

LCM = 28 HCF

Also, LCM + HCF = 1740

⇒ 28 HCF + HCF = 1740

⇒ 29 HCF = 1740 ⇒ HCF = \(\frac{1740}{29}=60\)

⇒ LCM = 28 × 60 = 1680

Since, one number = 240

∴ Other number = \(\frac{HCF \times LCM}{One\,number}\)

= \(\frac{60 \times 1680}{240}\) = 420