Question

Two numbers, both greater than 23, have HCF 23 and LCM 644. The sum of the numbers is:

Answer 1

Answer: 253

Step-by-step explanation:

First, we have two numbers A and B.

We know that all numbers can be written as a product of prime numbers.

And the HCF of A and B is 23

Then we can write:

A = 23*a

B = 23*b

(remember that 23 is a prime number)

Where a and b are larger than 1.

Now we know that the least common multiple between them is 644.

Notice that the primes that conform a can not be the same as the ones for b, because in that case, the HCF would not be 23.

Now to find a and b we can compute:

644/23 = 28.

28 = a*b

Now let's write 28 as a product of prime numbers:

a*b = 28 = 4*7 = 2*2*7

Then we can define:

a = 2*2

b = 7.

Our two numbers are:

A = 23*2*2 = 92

B = 23*7 = 161

A + B = 92 + 161 = 253