Question

find the greatest number of 5 digits exactly divisible by 12, 15 and 36

Answer 1

10080 is the smallest number

Answer 2

First we will.find the L.C.M of 12,15 and 36

12 = 2×2×3

15 =5×3

36 = 2×2×3×3

L.C.M = 22 × 32 × 5

L.C.M = 180

Now the largest 5 digit no. is 99999

Dividing the no. by L.C.M

99999/180 = 555.5

On multiplying 180 × 555

We will get 99900

We will check now and verify :

99900/12 = 8325

99900/15 =6660

99900/36 = 2775

Since it is divisible by all of them.

Therefore 99900 is the largest 5 digit no. which is divisible by 12,15 and 36.

Hope it helps.