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To be divisible by 3, 9, 5 and 10, a number must be a multiple of their lowest common multiple.

lcm(3, 9, 5, 10) = 90

So all multiples of 90 are divisible by 3, 9 5, and 10.

The first 4 digit number (excluding leading zeros) is 1000

→ 1000 ÷ 90 = 111/9 → first multiple of 90 ≥ 1000 is 12 x 90 = 1080

The last 4 digit number is 9999

→ 9999 ÷ 90 = 1111/10 → last multiple of 90 ≤ 9999 is 111 x 90 = 9990

→ all multiples of 90 between 12 and 11 (inclusive) are 4 digit numbers divisible by 3, 9, 5, 10, namely:

1080, 1170, 1260, 1350, 1440, 1530, 1620, 1710, 1800, 1890, 1980, 2070, 2160, 2250, 2340, 2430, 2520, 2610, 2700, 2790, 2880, 2970, 3060, 3150, 3240, 3330, 3420, 3510, 3600, 3690, 3780, 3870, 3960, 4050, 4140, 4230, 4320, 4410, 4500, 4590, 4680, 4770, 4860, 4950, 5040, 5130, 5220, 5310, 5400, 5490, 5580, 5670, 5760, 5850, 5940, 6030, 6120, 6210, 6300, 6390, 6480, 6570, 6660, 6750, 6840, 6930, 7020, 7110, 7200, 7290, 7380, 7470, 7560, 7650, 7740, 7830, 7920, 8010, 8100, 8190, 8280, 8370, 8460, 8550, 8640, 8730, 8820, 8910, 9000, 9090, 9180, 9270, 9360, 9450, 9540, 9630, 9720, 9810, 9900, 9990

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9y ago
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Wiki User

12y ago

One possible answer is 12,000.

12000/6 = 2000

While 12000/9 = 1333.33

(The three's continue to repeat.)

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11y ago

10296 is one.

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7y ago

81,818,180 of them.

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7y ago

100800

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Q: What is a 5 digit number divisible by 6 but not divsible by 9?
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