Answered

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

Sagot :

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]

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