The Gcd and lcm are 6 and 1080 respectively if the two numbers are 72 and 60,find the third number

Answer 1

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.