Determine the greatest 3-digit number exactly divisible by 8, 10 and 12.

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Solution

LCM of 8, 10, and 12

2

8, 10, 12

2

4, 5, 6

2

2, 5, 3

3

1, 5, 3

5

1, 5, 1

1,1,1

LCM = 2 × 2 × 2 × 3 × 5 = 120

We have to find the greatest 3-digit multiple of 120.

It can be seen that 120 ×8 = 960 and 120 × 9 = 1080.

Hence, the greatest 3-digit number exactly divisible by 8, 10, and 12 is 960.

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