Question
What is the greatest four digit number which is divisible by 15, 25, 40 and 75? [4 MARKS]
Answer:
:
Steps: 3 Marks
Answer: 1 Mark
The greatest number of 4-digits is 9999.
The prime factors of the given numbers are:
15=3×5
25=5×5
40=2×2×2×5
75=3×5×5
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.
∴ The LCM of the given numbers=2×2×2×3×5×5
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.
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:
Steps: 3 Marks
Answer: 1 Mark
The greatest number of 4-digits is 9999.
The prime factors of the given numbers are:
15=3×5
25=5×5
40=2×2×2×5
75=3×5×5
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.
∴ The LCM of the given numbers=2×2×2×3×5×5
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.
Was this answer helpful ?
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