Question

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 o

Answer 1

Let the HCF be x and LCM be 14x. So,
$x + 14x = 600 \\ 15x = 600 \\ x = 40$
Now, we know HCF = 40, so LCM = 14x = 14*40 = 560
Now we know, product of HCF and LCM = product of the numbers.
One number is 280, and other number be x. So,
$560 \times 40 = 280 \times x \\ x = (560 \times 40) \div 280 \\ x = 2 \times 40 \\ x = 80$
Therefore, other number is 80.