Question

Find the smallest number which when divided by 8,12,15,18 and 24 leaves as remainder. Please answer fast

Answer 1

Answer:

Step-by-step explanation:

Find the LCM of 8,12,15,18 and then add 24 to it.

LCM is 360

Add 24

Therefore answer is 384

Answer 2

Answer:

The least number is 360

Step-by-step explanation:

The least number which is exactly divisible by each given number is their L.C.M.

$2| 8,12,15,18,24\\2| 4,6,15,9,12\\2| 2,3,15,9,6\\3| 1,3,15,9,3\\3| 1,1,5,3,1\\5| 1,1,5,1,1\\1 | 1,1,1,1,1$

Bring down any numbers that are not evenly divisible by the prime number.

When the last row of results is all 1's you are done.

Find the product of the prime numbers in the first column to get the LCM:

LCM = 2 x 2 x 2 x 3 x 3 x 5

LCM = 360

Therefore,

LCM(8, 12, 15, 18, 24) = 360

Method2:

Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

Multiples of 8:

8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376

Multiples of 12:

12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384

Multiples of 15:

15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390

Multiples of 18:

18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234, 252, 270, 288, 306, 324, 342, 360, 378, 396

Multiples of 24:

24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, 384, 408

Therefore,

LCM(8, 12, 15, 18, 24) = 360