Question

Numerical & Mental Ability
Q.86
+2.5. -0.0
The LCM of two numbers is 114 times their HCF. If the
sum of LCM and HCF is 2300 and one of the numbers is
380, find the other number.​

Answer 1

Answer:

120

Step-by-step explanation:

LCM = 114 × HCF … (1)

LCM + HCF = 2300 … (2)

By equating (1) and (2)

114 × HCF + HCF = 2300

⇒ 115 × HCF = 2300

⇒ HCF = 20

Now

LCM = 114 × 20

⇒ LCM = 2280

One of the numbers is (A) = HCF × (a)

⇒ 380 = 20 × (a)

⇒ (a) = 19

Let

Other number (B) = HCF × (b)

LCM = HCF × (a) × (b)

⇒ 2280 = 20 × 19 × (b)

⇒ (b) = 6

So other number (B) = HCF × (b)

⇒ other number(B) = 20 × 6

∴ other number = 120