The Gcd and lcm are 6 and 1080 respectively if the two numbers are 72 and 60,find the third number
Let the third number be 'x'.
We know that,
GCD of 72, 60 and x = 6
Therefore, we can write:
72 = 2^3 * 3^2
60 = 2^2 * 3 * 5
GCD = 2^2 * 3 = 12
So, x must also contain factors of 2^2 and 3.
Now,
LCM of 72, 60 and x = 1080
We can write,
LCM = 2^3 * 3^2 * 5 * x/GCD
1080 = 2^3 * 3^2 * 5 * x/12
Simplifying,
90 = x/2
Therefore,
x = 180
Hence, the third number is 180.