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The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one number is 280, then find the other number.
LCM of the two numbers a and b is the least number which is exactly divisible by both the numbers a and b.
Answer: The other number is 80
Let's assume the LCM and HCF of the two numbers are 'x' and 'y' respectively.
Then, x = 14y, and x + y = 600
Substitute x = 14y in the equation x + y = 600 and find the values of 'y'.
x + y = 600
14y + y = 600
15y = 600
y = 600/15
y = 40
Now substitute y = 40 in equation x = 14y and find the value of 'x'
x = 14y
x = 14 × 40
x = 560
Therefore, the LCM and HCF of the two numbers are 560 and 40 respectively.
Now use the formula LCM (a,b) = (a × b) / HCF (a,b) and substitute a = 280, 560 for LCM(a, 280) and 40 for HCF(a, 280), to calculate the another number 'a'
LCM (a,b) = (a × b) / HCF (a,b)
560 = (a × 280) / 40
560 = a × 7
a = 560/7
a = 80
Thus, the other number is 80.