Question

The HCF of two numbers is 175. The LCM of these two numbers is 12600. Both numbers are greater than their HCF. Find the two numbers

Answer 1

Hello,

Answer : 1400 and 1575

Explanation:

Let's say a and b the ywo numbers

`HCF(a,b)=a\vee b=175=5^2*7\\LCM(a,b)=a\wedge b=12600\\\\a*b=(a\vee b)*(a\wedge b)=(2^3*3^2*5^2*7)*(5^2*7)=2^3*3^2*(5^2*7^2)^2\\\\Both\ numbers\ are\ greater\ than\ their HCF\\a=175*k_1\\b=175*k_2\\\\k_1=2^3\ and\ k_2=3^2\\\\a=175*2^3=1400\\b=175*3^2=1575\\\\`