Question

Find the lowest number between 200 and 500 which a remainder of 3 in each case when divided by 8 ,10,12,30

Answer 1

the lowest number between 200 And 500 which When divided by 8,10,12,30 leaving remainder 3 will be
LCM of these + 3
8=2³
10=2×5
12=2²×3
30=2×3×5
LCM=2³×3×5=120
we need to find number between 200 and 500
so 120×2=240
required number =240+3=243

Answer 2

243 is the lowest number between 200 and 500 which a remainder of 3 in each case when divided by 8 ,10,12,30

Solution:

Given that,

We have to find the lowest number between 200 and 500 which a remainder of 3 in each case when divided by 8 ,10,12,30

Step 1:

FIND LCM OF 8 ,10,12,30

List all prime factors for each number.

Prime Factorization of 8 is:   2 x 2 x 2  

Prime Factorization of 10 is:   2 x 5

Prime Factorization of 12 is:   2 x 2 x 3  

Prime Factorization of 30 is:    2 x 3 x 5  

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

2, 2, 2, 3, 5

Multiply these factors together to find the LCM

LCM = 2 x 2 x 2 x 3 x 5 = 120

LCM = 120

STEP 2:

Number should lie between 200 and 500

We know that,

$120 \times 1 = 120\\\\120 \times 2 = 240$

Now, add 3 in 240, as we need a number which leaves a remainder

240 + 3 = 243

Thus, 243 is the lowest number between 200 and 500 which a remainder of 3 in each case when divided by 8 ,10,12,30

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