Question

what is the least whole number that has the remainders 10,12, and 15 when divided by 16, 18. and 21, respectively

Answer 1

`1002`

Explanation:

First find difference between the divisors and remainders.

`16-10=6\\18-12=6\\21-15=6`

Here, the difference between the divisors and remainders is equal.

So, the required number is equal to LCM of
`(16,18,21)-6`

`16=2^4\\18=2(3^2)\\21=3(7)`

LCM of
`(16,18,21)=2^4(3^2)(7)=1008`

Required Number
`=1008-6=1002`