Question

Find the least number of four digits which is exactly divisible by 24 30 32 and 36

Answer 1

The number that I came up with was 9,072. I found the LCM (Least Common Multiple) using Prime factorization which was 1,008 but you wanted the highest 4 digit number so I multiplied 1,008 to the highest whole number that would still render a 4 digit answer, which was 9 (1,008 * 9 = 9,072).

12 = 2 x 2 x 3

16 = 2 x 2 x 2 x 2

24= 2 x 2 x 2 x 3

28 = 2 x 2 x 7

36 = 2 x 2 x 3 x 3

LCM = 2 x 2 x 2 x 2 x 3 x 3 x 7 = 1,008

1,008 x 9 = 9,072

9,072 is divisible by 12(756), 16 (567), 24 (378), 28 (324), & 36(252)