Question

Find the greatest 4 digit number divisible by 12,16,24,28 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)

I hope that helps!



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OTHER ANSWERS




Let us first calculate its L.C.M

12=2*2*3

16=2*2*2*2

24=2*2*2*3

28=2*2*7

36=2*2*3*3

Therefore l.c.m

2*2*3*7*3*2*2=1008

Now greatest no of 4 digit is 9999

Let us divide 9999 by 1008

Then we will have 927 as reminder

So if we subtract 927 from 9999 then the result must be divisible by 1008 i.e the lcm of the given no.s i.e esch of the no.s.

So our number will be 9999–927=9072..








12=2×2×312=2×2×3

16=2×2×2×216=2×2×2×2

24=2×2×2×324=2×2×2×3

28=2×2×728=2×2×7

36=2×2×3×336=2×2×3×3

The greatest number divisible by 12, 16, 24, 28, and 36 is

2×2×2×2×3×3×7=10082×2×2×2×3×3×7=1008

1008×9=9072