What is the least multiple of 23 which when divided by 18,21 and 24 leaves remainders 7, 10
and 13 respectively?
Answers
Take L. C. M of given no 18,21 and 24
2- use the formula
L.C.M×M−R=23×n
where R is
no. of term
sum of reminders
and M,n are variable
3- use the hit and trial method by putting the values M and check whether the no is divided by 23 or not
we have to find the LCM of the divisors i.e.18,21 and 24.
The LCM of 18, 21 and 24 is 504
and
if we subtract 11 from it, we get 493 and this is the required number that leaves the remainders 7, 10 and 13 with the divisors 18, 21 and 24 respectively.
Now, we have 2 variables and there’s only 1 equation, so obviously we are going to have infinite solutions and we will have to proceed with the trial and error method to obtain the first solution.
If we try with M as 1, we get a number that leaves 10 as the remainder with 23. If we try with M as 2, we get a number that leaves 8 as the remainder with 23. So we expect 0 as the remainder when M=6.
If we try with M as 6, indeed we get 0 as the remainder with the number 504×6–11=3013
Hence required number is 3013.
hope this help for solving your problem .
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