Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.

Question:

Find the greatest number of four digits which is exactly divisible by 15, 24 and 36.

Solution:

Prime factorization:

15 = 3 × 5

$24=2^{3} \times 3$

$36=2^{2} \times 3^{2}$

LCM = product of greatest power of each prime factor involved in the numbers $=2^{3} \times 3^{2} \times 5=360$

Now, the greatest four digit number is 9999.
On dividing 9999 by 360 we get 279 as remainder.
Thus, 9999 − 279 = 9720 is exactly divisible by 360.

Hence, the greatest number of four digits which is exactly divisible by 15, 24 and 36 is 9720.

 

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