How many numbers between 111 and 100100100 (inclusive) are divisible by 333 and 101010?

Solution:

Given, the numbers between 111 and 100100100 (inclusive) are divisible by 333 and 101010.

We have to find the total numbers that are divisible by 333 and 101010.

Total number divisible by 333 = 100100100/333

= 300600

Total number divisible by 101010 = 100100100/101010

= 990

Numbers that are divisible by both 333 and 101010 can be found by 100100100/LCM of 333, 101010

Factors of 333 = 3 × 111

Factors of 101010 = 910 × 111

Now, LCM = 3 × 111 × 910

= 303030

So, 100100100/303030 = 330

Numbers between 111 and 100100100 (inclusive) are divisible by 333 and 101010 = 300600 + 990 - 330

= 300600 + 660

= 301260

Therefore, the required value is 301260.

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How many numbers between 111 and 100100100 (inclusive) are divisible by 333 and 101010?

Summary:

The numbers between 111 and 100100100 (inclusive) are divisible by 333 and 101010 are 301260.