Math, asked by srivastavavibha385, 9 months ago

greatest 4 digit number which is exactly divisible by 4, 6, 12 ​

Answers

Answered by ssaharshyadav
0
We know that the Greatest number of four digits = 9999


To find the greatest number of 4 digit we have to find the L.C.M of 12, 18, 40,45

Prime factorization :
12= 2×2×3= 2²×3¹

18= 2×3×3= 2¹× 3²

40= 2×2×2×5= 2³×5

45= 3×3×5= 3²×5

L.C.M of 12 ,18,40,&45= 2³×3²×5


L.C.M of 12 ,18,40,&45= 2×2×2×3×3×5

L.C.M of 12 ,18,40,&45= 360

Now divide the largest 4 digit number 9999 by 360

9999 ÷ 360

9999= 360× 27 +279

Remainder= 279

Then Subtract the remainder from 9999

9999- 279= 9720

Hence, greatest number of four digits which is divisible by 12, 18, 40 & 45
= 9720
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