Question

find the smallest 6 digit number which is exactly divisible by 8 15 and 18​

Answer 1

Answer:

The smallest 6 digit number which is exactly divisible by 8 15 and 18 is 100080.

Step-by-step explanation:

The elements of quite a number are numbers that frivolously divide into it. A top aspect is a aspect this is best divisible through 1 and itself. You can use a aspect tree that will help you discover a number's top factorization.

$8 = 2 × 2 × 2 \\ </p><p>15 = 3 × 5 \\ </p><p>18 = 2 × 3 × 3$

LCM of numbers is the smallest not unusualplace more than one or a effective integer that is divisible absolutely with the aid of using each the numbers. LCM is the least not unusualplace more than one among or extra numbers that is completely divisible with the aid of using them. Suppose the LCM of a and b is same to c, then c have to be flippantly divisible with the aid of using each a and b.

Hence,

LCM of 8 , 15 and 18 is

$2³ × 3² × 5 \\ = 360$

smallest 6 Digit number is

100000

$100000 ÷ 360 = 277.78$

Rounding off 277.78 to 280.

Hence ,

$280× 360 \\ = 100080$

hence ,

smallest 6 digit number which is exactly divisible by 8 15 and 18 is 100080.

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Answer 2

Answer:

The smallest 6 digit number which is exactly divisible by 8 15 and 18​ = 100080

Step-by-step explanation:

To find,

The smallest 6 digit number which is exactly divisible by 8,15,18

Solution:

Recall the concept,

The smallest number which is exactly divisible by the given numbers is the LCM of the numbers

All the numbers which are exactly divisible by the given numbers are the product of the LCM of the numbers.

Here, the given numbers are 8,15 and 18

To find LCM(8,15,18)

The prime factorization of 8 = 2×2×2

The prime factorization of 15 = 3×5

The prime factorization of 18 = 2×3×3

The  LCM(8,15,18) = 2×2×2×3×3×5 = 360

The least number which is exactly divisible by 8,15, and 18 = 360

All the numbers which are exactly divisible by 8,15, and 18 are the multiples of 360.

Hence, the smallest six digit number which is exactly divisible by 8,15 and 18, is the smallest six digit number exactly divisible by 360

The smallest six digit number is 100000

Then by division algorithm we have,

100000 = 360×277 + 280

100000 - 280 = 360×277, is divisible by 360

The next number divisible by 360 is 100000 - 280 +360 = 100080

Hence, the smallest 6 digit number which is exactly divisible by 8 15 and 18​ = 100080

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