Explanation This is one of the best Questions on HCF and LCM,
Try to grasp it properly!
3240 = 2x2x2x3x3x3x3x5 = 2^{3 }x 3^{4 }x 5
3600 = 3x3x2x2x2x2x5x5 = 2^{4} x 3^{2 }x 5^{2}
HCF of 3240 and 3600 and = 2^{3} x 3^{2}
So the third number must have (2^{3} x 3^{2} ) ---------- (1)
The LCM of the three numbers is 2^{4} x 3^{5} x 5^{2} x 7^{2}.
LCM is the product of all the common prime factors raised to their highest power.
and out of the LCM 2^{4} x 5^{2} is taken from the first two numbers,
It means the third number must contain the remaining factors in the LCM i .e. 3^{5} x 7^{2 }------(2)
Using (1) and (2), we get the third number as :
2^{3} x 3^{5} x 7^{2 .}