Answer: 253
Step-by-step explanation:
We begin with two numbers, A and B.
Every number can be expressed as the product of prime factors.
The HCF of A and B is 23.
Thus, we can express them as:
A = 23*a
B = 23*b
(it's important to note that 23 is prime)
Where a and b must both be greater than 1.
We also know that their least common multiple is 644.
It should be pointed out that the prime factors of a cannot overlap with those of b, as that would mean the HCF wouldn't remain 23.
To solve for a and b, we calculate:
644/23 = 28.
This implies that a*b = 28.
Next, we can write 28 as a product of prime numbers:
a*b = 28 = 4*7 = 2*2*7
This allows us to define:
a = 2*2
b = 7.
Consequently, our two numbers are:
A = 23*2*2 = 92
B = 23*7 = 161
Adding them, A + B = 92 + 161 = 253
