Question

find the least multiple of 23 which when divided by 18 21 24 leaves remainder 7 10 13 respectively

Answer 1

LCM of 18, 21 and 24 is 504 then 18-7=11 21-10=11 24-13=11 so common is 11 Require number is (504m 11)/23 (504*6 11)/23 = 3013

Answer 2

Answer :-

Subtract the remainders from their respective divisors :-

■ 18 - 7 = 11

■ 21 - 10 = 11

■ 24 - 13 = 11

LCM of 18, 21 and 24 = 504

Number = $\sf{504m - 11}$

Least value of m for which, this number will be divisible by 23 is = $\sf{6}$

Number = 504 × 6 - 11

=》 $\huge{\sf{3013}}$