Identify Prime Factors of LCM

The question states that the LCM of two prime numbers, $x$ and $y$, where $x > y$, is 319. Since $x$ and $y$ are distinct prime numbers, their LCM is simply their product.

Therefore, we need to find the prime factors of 319.

We can test small prime numbers to find the factors of 319:

• $319 \div 11 = 29$

Both 11 and 29 are prime numbers.

Determine Values of x and y

We found the prime factors of 319 are 11 and 29. The question specifies that $x > y$. Assigning the larger factor to $x$ and the smaller factor to $y$:

• $x = 29$
• $y = 11$

Calculate the Expression 2x - 5y

Now substitute the values of $x$ and $y$ into the expression $2x - 5y$:

$2x - 5y = 2(29) - 5(11)$

Calculate the terms:

• $2 \times 29 = 58$
• $5 \times 11 = 55$

Perform the subtraction:

$58 - 55 = 3$

The value of the expression $2x - 5y$ is 3.