Question

How many numbers between 100 and 500 are divisible by 4, 5 and 6?
1. 6
2. 10
3. 5
4. 7

Answer 1

Correct Answer - Option 4 : 7

Concept used:
In Arithmetic progression,
an = a1 + (n – 1) × d

Calculation:
Taking L.C.M. of 4, 5 and 6 = 60
Dividing 500 by 60, we get the remainder as 20.
Subtracting 500 from 20, we get 480.
Dividing 100 by 60, we get remainder ad 40. 
Subtracting 100 from 40, we get 60
The term which is divisible by 60 and greater than 100 is 120.
First term (a₁) = 120
Last term (a_n) = 480
Let number of terms divisible by 60 be n.
⇒ 480 = 120 + (n – 1) × 60
⇒ 480 – 120 = (n – 1) × 60
⇒ 360/60 = n – 1
⇒ 6 = n – 1
⇒ n = 7
∴ 7 numbers between 100 and 500 are divisible by 4, 5 and 6.