Question

The greatest 4-digit number that is a common multiple of 12,40 ,45

Answer 1

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, 40, 45

Prime factorization :

12= 2×2×3= 2²×3¹

40= 2×2×2×5= 2³×5

45= 3×3×5= 3²×5

L.C.M of 12 ,40,&45= 2³×3²×5

L.C.M of 12 ,40,&45= 2×2×2×3×3×5

L.C.M of 12 ,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, 40 & 45

= 9720