Question

HCF of 3240,3600 and a third number is 36 and their LCM is 4762800.Find out
the third number.​

Answer 1

Answer:

Given: a= 3240

b= 3600

HCF= 36

Find: c=?

Solution:

3240 = $2^{2} * 3^{4} * 5$

3600 = $2^{4}* 3^{2} * 5^{2}$

36= $2^{2} *3^{2}$

Since HCF is the product of the lowest powers of common factors, so the third number must have $(2^{2} *3^{2} )$ as its factor.

Since LCM is the product of highest powers of common prime factors, so the third number must have $3^{5}$ and $7^{2}$ as its factors.

Third number= $2^{2} *3^{5}* 7^{2}$

c= $2^{2} *3^{5}* 7^{2}$

The third number will be 47628.