Question

what is the least number when divided by 98 and 105 has in each case 10 as remainder. ​

Answer 1

Answer:

The least number which when divided by 98 and 105 will leave the remainder 10 is 1480.

We have to find the least number which when divided by 98 and 105 leaves the same remainder 10.

Let the least number be x.

Therefore, when x is divided by 98 and 105 both the division leaves behind the same remainder 10.

Therefore the least number which will be divided by 98 and 105 both will be x - 10.

The LCM of 98 and 105 is x - 10.

Evaluating the LCM of 98 and 105.

98 = 2 × 7 × 7

105 = 3 × 5 × 7

LCM = 2 ×3 × 5 × 7 × 7 = 1470

Now,

x-10 = 1470

x = 1470 + 10 = 1480

Therefore the least number which when divided by 98 and 105 will leave the remainder 10 is 1480.

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Answer 2

Answer:

4180

Step-by-step explanation:

LCM OF 98 AND 105

2 I 98 , 105

3 I 49 , 105

7 I 7 , 35

7 I 1 , 5

5 I 1 , 1

= 2×3×5×7×7

= 6×35×7

= 42×35

= 1470

1470 + x = ?

1470 + 10 = 1480 ( as we want 10 as remainder )

= 1470

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