Given, the HCF of two numbers is 16 and their product is 3072.

Let the two numbers be a and b.


To find the numbers, we need to factorize the product of the numbers.

3072 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Now, we need to find two numbers whose product is 3072 and HCF is 16.

We can write 3072 as a x b, where a and b are the two numbers.

So, a x b = 3072

Let us write the prime factorization of a and b.

a = 2 x 2 x 2 x 2 x 2 x 2 x 2 x p

b = 2 x 2 x 2 x 2 x 2 x 2 x 2 x q

where p and q are some other prime factors.

Now, we know that HCF of a and b is 16.

So, HCF(2 x 2 x 2 x 2 x 2 x 2 x 2 x p, 2 x 2 x 2 x 2 x 2 x 2 x 2 x q) = 16

So, the HCF of p and q should be 1.

Therefore, p and q should not have any common factor other than 1.

We can take p = 3 and q = 5.

So, a = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 = 768

b = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 = 1920

Therefore, the two numbers are 768 and 1920.


To find the LCM of two numbers, we need to find the product of their prime factors, taking the highest power of each prime factor.

Prime factors of 768 = 2 x 2 x 2 x 2 x 2 x 2 x 3

Prime factors of 1920 = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 3

So, the LCM of 768 and 1920 can be calculated as follows:

LCM = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5

LCM = 960

Therefore, the LCM of 768 and 1920 is 960.

Given = Product of 2 no. is = 3072

H.C.F = 16

Find = LCM

Solution = We know that product of two numbers is equal to the product of their HCF and LCM.

a × b = HCF ( a,b ) × LCM ( a,b )

3072 = 16 × LCM

LCM = 3072/16 = 192

LCM is 192.