Question

Find the least number which when divided by 98 and 105 will leave in each case the same remainder 10

Answer 1

LCm. of 98 and 105 =1470

number is 1470.+10 = 1480

Answer 2

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.