Answer:
[tex]1002[/tex]
Step-by-step explanation:
First find difference between the divisors and remainders.
[tex]16-10=6\\18-12=6\\21-15=6[/tex]
Here, the difference between the divisors and remainders is equal.
So, the required number is equal to LCM of [tex](16,18,21)-6[/tex]
[tex]16=2^4\\18=2(3^2)\\21=3(7)[/tex]
LCM of [tex](16,18,21)=2^4(3^2)(7)=1008[/tex]
Required Number [tex]=1008-6=1002[/tex]
