solution to question paper 1 -- IPM STD V

How many numbers between 281 and 651 are divisible by 2,3,4, and 5?

Answer:

The LCM of 2,3,4, and 5 is 60.

We will find the total number of integers that are completely divisible by 60, upto 281.

i.e. 281 / 60 = 4 ⁴¹/₆₀. So, only 4 integers.

We will find the total number of integers that are completely divisible by 60, upto 651.

i.e. 651 / 60 = 10 ⁵¹/₆₀. So, only 10 integers.

Therefore, between 651 and 281, we have 10 – 4 = 6 integers.