the LCM of 2 numbers is 14 times their HCF . the sum of LCM and HCF is 600 . if one number is 280 , then find the other number
Answers
Answer:
80
Step-by-step explanation:
Let the other number be ′x′
Given:LCM+HCF=600
⇒14HCF+HCF=600
⇒15HCF=600
⇒HCF=40
⇒LCM=14×40=560
we know that, HCFxLCM=Product of 2 numbers
=>40×560 = 280×x
=>X=(40x560)÷280
⇒x=80
hence the other number is 80.
Step-by-step explanation:
Given:-
The LCM of 2 numbers is 14 times their HCF .
The sum of LCM and HCF is 600 .
One number is 280 .
To find:-
Find the other number ?
Solution:-
Let the other number be b
Given that
One number = (a) = 280
The LCM of two numbers = 14 times thier HCF
=> LCM = 14× HCF
=> L = 14 H ------------(1)
and
The sum of the LCM and the HCF = 600
=> LCM + HCF = 600
=> L+H = 600 ----------(2)
On Substituting the value of L in (2)
=> 14H + H = 600
=> 15 H = 600
=> H = 600/15
=> H = 40
HCF = 40
On Substituting the value of H in (1)
=> L = 14×40
=> L = 560
LCM = 560
Now , we Know that
LCM × HCF = Product of two numbers
=> L× H = a×b
=> b = (L×H)/a
=> b = (560×40)/280
=> b = 2×40
=> b = 80
Answer:-
The other number for the given problem is 80
Used formulae:-
- LCM × HCF = Product of two numbers