Question

how many numbers between 200 and 400 are divisible by 3, 5 and 6

Answer 1

Numbers between 200 and 400

Find the number of terms that are divisible by 3:

Smallest number = 201

Largest number = 399

Common difference = 3

an = a1 + (n - 1)d

399 = 201 + (n - 1)3

339 = 201 + 3n - 3

3n = 201

n = 67

Find the number of terms that are divisible by 5:

Smallest number = 205

Largest number = 395

Common difference = 5

an = a1 + (n - 1)d

395 = 205 + (n - 1)5

395 = 205 + 5n - 5

5n = 195

n = 39

Find the number of terms that are divisible by 6:

All numbers that are divisible 6 are also divisible by 3.

∴ the numbers of terms have been included in the divisible by 3 calculation.

Find the total number of terms:

Total number of terms = 67 + 39 = 106

Answer: There are 106 numbers that are divisible by 3, 5 and 6

Answer 2

Answer:

7

Step-by-step explanation: LCM=3,5,6

                                                      =30

7*30=210

8*30=240

9*30=270,

10*30=300

11*30=330

12*30=360

13*30=390