Question

If the least common multiple of 85 and 255 can be expressed as 85R+255, then the value of R is:

• A. 10
• B. 0
• C. 6
• D. 14

Answer 1

Answer:

B. 0

The value of R is 0.

Prime Factorisation

To find the least common multiple (LCM), we first determine the prime factors of both numbers:

• 85: $5 \times 17$

• 255: $3 \times 5 \times 17$

Least Common Multiple (LCM) Calculation

The LCM is calculated by taking the highest power of each prime factor involved:
$\text{LCM}(85,255)=3\times 5\times 17=255$

Since 255 is a direct multiple of 85, $85 \times 3 = 255$, the LCM is simply 255.

Linear Equation Solution

We are given that the LCM can be expressed in the form 85R + 255. Set the expression equal to the calculated LCM:
85R+255=255

Subtract 255 from both sides:
85R=0

Divide by 85:
R=0