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

Mathematics

1 answer:

AnnZ [28]2 years ago

7 0

Answer:

$1002$

Step-by-step 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 $=1008-6=1002$

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