Question

Find the greatest 5-digit number which is exactly divisible by 9, 15 and 18
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Answer 1

Answer:

First find the least common multiple of 12, 15, 18

You could make a list of the multiples of each number until you find the same number in all three lists. But that could take a long time depending on the numbers.

Hopefully you know how to find the prime factorization of each number (dividing only by primes (2, 3, 5, 7, 11, 13, etc.) until the answer is 1).

In this case:

12 = 2 X 2 X 3 or 2^2 X 3

15 = 3 X 5

18 = 2 X 3 X 3 or 2 X 3^2

The LCM is found by taking ALL the different prime factors

here 2, 3, 5

and taking each to the largest power listed

here 2^2 or 4, 3^2 or 9, and 5

Multiply those together 4 X 9 X 5 = 180 (this is the LCM of 12, 15, 18)

To answer the question of the largest 5 digit multiple (or exactly divisible by):

The largest 5 digit number is 99999

Divide that by the LCM of 180 99999/180 = 555.55

Take the whole number part 555 because you want exactly divisible by and multiply it by the LCM: 555 X 180 = 99900

99900 IS THE LARGEST 5 digit NUMBER DIVISIBLE BY 12, 15, 18

Step-by-step explanation:

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