Question

Determine the largest 4-digit number that is exactly divisible by 15,25,40 and 75.

• A. 9600
• B. 9975
• C. 9999
• D. 9960

Answer 1

Answer:

A. 9600

To find the largest 4-digit number exactly divisible by 15, 25, 40, and 75, follow these steps:

Prime factorization:

$(15 = 3 \times 5)$

$(25 = 5^2)$

$(40 = 2^3 \times 5)$

(75 = 3 \times 5^2)#

LCM takes highest powers:

\text{LCM} = 2^3 \times 3 \times 5^2 = 8 \times 3 \times 25 = 600$</p><h3 style="color: rgb(0,0,0);"></h3><p data-pxy="true" style="color: rgb(0,0,0); margin-top: 2px; margin-bottom: 2px;">Largest 4-digit number = 9999</p><p data-pxy="true" style="color: rgb(0,0,0); margin-top: 2px; margin-bottom: 2px;"><br>$\frac{9999}{600} \approx 16.66$</p><p data-pxy="true" style="color: rgb(0,0,0); margin-top: 2px; margin-bottom: 2px;">So the greatest integer multiple is <b>16</b>:<br><br>$600 \times 16 = 9600$

9600 is the largest 4-digit number exactly divisible by 15, 25, 40, and 75.