Problema Solution
What is the greatest five digit number which when divided by 12, 15, 18 and 27 leaves a remainder 3 in each case?
Answer
A) 99000
B) 90999
C) 89999
D) None of the above
A) Approx 66138 lb
B) Approx 33069 lb
C) Approx 2578 lb
D) Approx 7128 lb
Answer provided by our tutors
D) None of the above
Explanation:
A number that when divided by 12,15, 18 and 27 will leave a remainder of 3 will be 3 more than a multiple of lowest common multiple of the 3 numbers.
How do you find the lowest common multiple? Well, one way is to multiply the 4 numbers together and divide by the greatest common factor (in this case we see all 4 numbers are divisible by 3.
lcm(12, 15, 18, 27) = 12 x 15 x 18 x 27 / 3 = 21960.
Five-digit multiples of this are 58320 and 87480.
The greatest 5 digit number that is divisible by 12, 15, 18 and 27 is 87480. Add 3 to find that the greatest 5-digit nubmer which when divided by 12, 15, 18 and 27 leaves a remainder of 3 is 87483.