Question

largest number of 4 digits divisible by 10, 12, and 18. ...it is not 8 it is 18teen ... please tell me exact answers​

Answer 1

Answer:

see below

Step-by-step explanation:

In this question, to find the largest number which will be exactly divisible by the given numbers, find their LCM by finding the factors and divide the LCM with the largest number 9999 to check whether they are divisible and if not find the difference.

Given the numbers are 12, 15, 18 and 27

The largest 4 digit number known is 9999

For largest number find the LCM by factorizing of the numbers

2|12,15,18,27−−−−−−−−−−3|6,15,9,27−−−−−−−−−3|2,5,3,9−−−−−−−2,5,1,3

Hence the factors of each number are:

12=2×3×215=3×518=2×3×327=3×3×3

So the LCM of the three numbers will be:

LCM(12,15,18,27)=2×2×3×3×3×5=540

Hence the LCM of numbers 12,15,18,27

is540

Now check whether the 4 digit greatest number is divisible by 540

On dividing9999540=18279540

, 279 is the remainder; hence we can say 9999 is not exactly divisible by 540, hence subtract

(9999−279)=9720

The number is exactly divisible by 540 hence 9720 is the largest 4 digit number divisible by 12, 15, 18 and 27