Question

find the least no.which when divided by 16,36,40leaves remainder 5 as remainder each case.

=LCM of 16,36,40=720
720+5=725.ANS.​

Answer 1

Solution:

$\frac{x}{16} = 5 \: \: \: \: \frac{x}{36} = 5 \: \: \frac{x}{40} = 5$

To find x we need to :

$16 - 5 = 11 \\ 36 - 5 = 31 \\ 40 - 5 = 35$

Three numbers are :11,31,35

LCM of these three numbers = 11935

Therefore:

11935 is the least number which when divided by 16,36 , 40 leave remainder 5 as remainder each case.

Answer 2

GiveN:

A least number when divided by 16,36,40 leaves remainder 5 as remainder in each case.

To FinD:

• least number?

SolutioN:

let's find the prime factors of 16 , 36 , 40:

16 = 2 × 2 × 2 × 2

36 = 2 × 2 × 3 × 3

40 = 2 × 2 × 2 × 5

gathering all the nessasary factors :

LCM = 2 × 2 × 2 × 2 × 3 × 3 × 5 = 720

add 5 , ( The remainder for each division )

LCM = 720 + 5 = 725

we are done!

Your answer is correct ✓

ThereforE

725 is he least number which when divided by 16 , 36 , 40 leaves 5 as

remainder in each case.