Question

What is the least number which when divided by 16, 18, 20 and 25 leaves 4 a the remainder in each case but when divided by 7 leaves no remainder
please explain

Answer 1

answer

18004

explanation

LCM of 16, 18, 20, 25 = 2×5×2×5×3×3×2×2

= 3600

As in each case the reminder is 4 we, add 4 to

3600 to get 3604 . but it is not divisible by 7 .

so , we can write the number as 3600k+4

when k = 2,

3600×2+4 = 7204

which is not divisible by 7

then k = 3

3600×3+4 = 10804

not divisible by 7

k= 4

3600×4+4 = 14404

not divisible by 7

k= 5

3600×5+5 = 18004

which is divisible by 7.

so, 18004 is the least number which is divisible by 16,18,20,25 and leaves 4 as remainder and is divisible by 7.