Question

5. What least number and what greatest number
must be subtracted from 23759143 so that the
remainders may be divisible by 24, 35, 91,
130 and 150 ?​

Answer 1

Step-by-step explanation:

24 = 2x2x2x3

35 = 5x7

91 = 7x13

130 = 2x5x13

150 = 2x3x5x5

So LCM = 2x2x2x3x5x5x7x13 = 54600

Next divide 23759143 by 54600 to get 435.1491392.

From the quotient deduct 435 to get 435.1491392 - 435 = 0.1491392.

Next multiply 0.1491392 by 54600 to get 8143.

Next take the next integer higher than 435.1491392 which is 436.

Multiply 436 by 54600 to get 23805600 which is higher than 23759143 by

23805600 - 23759143 = 46457.

So you need to deduct 8143 from 23759143 to get 23751000 which is divisible by 24, 35, 91, 130 and 150.

So you need to add 46457 to 23759143 to get 23805600 which is divisible by 24, 35, 91, 130 and 150.

Answer: Deduct 8143 or add 46457 to 23759143 to get the resulting numbers as - 23751000 and 23805600 - both of which are divisible by 24, 35, 91, 130 and 150.