Question

What least number being divided by 18, 20, 24 and 30 will leave the remainders
15, 17, 21 and 27 respectively?
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Answer 1

Answer:

I thought it will help you a lot

Please comment how is it ????

Step-by-step explanation:

The smallest number which when divided by 18, 24, 38 and 42 leaves the remainder 15, 21, 35 and 39 respectively is?

Let the smallest number be X.

First, let's find the LCM of given numbers

As you can see in above image,

We got LCM = 9576

Difference between divisor and reminder is

18–15=3

24–21=3

38–35=3

42–39=3

So the difference is common for all which is 3

LCM - Difference

= 9576 - 3

= 9573

9573 is the smallest possible number

Answer 2

Question:-

What least number being divided by 18, 20, 24 and 30 will leave the remainders

15, 17, 21 and 27 respectively?

solutions:-

Let the no of division = X

LCM of 18, 20 , 24, 30 =

To find :-

LCM :-

$18 = | 2| \times(3) \times 3 \\ 20 = |2| \times |2| \times (5) \\ 24 = |2| \times |2| \times 2 \times (3) \\ 30 = |2| \times( 3 )\times (5)$

now

find the same number and other number for answer of LCM

there is bracket | | , ( ) like this these number are same and this number multiply only one time

given

$lcm \: = \\ 2 \times 2 \times 2 \times 3 \times 3 \times 5 \\ = > 360$

therefore,

The number required = 360 - X

then ,

find the difference of LCM

$18 - 15 = 3 \\ 20 - 17 = 3 \\ 24 - 21 = 3 \\ 30 - 27 = 3$

difference is 3

Answer :-

$360 - 3 \\ 357$

required = 357

Thanks