Question

What is the greatest four digit number which is divisible by 15, 25, 40 and 75? [4 MARKS]

Answer 1

Steps: 3 Marks
Answer: 1 Mark

The greatest number of 4-digits is 9999.
The prime factors of the given numbers are:
15=3$\times$5
25=5$\times$5
40=2$\times$2$\times$2$\times$5
75=3$\times$5$\times$5
The maximum number of times the prime factor 2 occurs is 3.
The maximum number of times the prime factor 3 occurs is 1.
The maximum number of times the prime factor 5 occurs is 2.
$\therefore$ The LCM of the given numbers=2$\times$2$\times$2$\times$3$\times$5$\times$5

L.C.M. of 15, 25, 40 and 75 is 600.

On dividing 9999 by 600, the remainder is 399.

Required number (9999 - 399) = 9600.