Question

Find the least natural number which when divided by 112, 140 and 168 leaves 5 as remainder in each case.

Answer 1

Here is your answer!!!

Answer:

LCM pf 112,140and 168 is 1680

Step-by-step explanation:

1680+8

=1688

Therefore 1688 is the least natural number which when divided by 112, 140 and 168 leaves 5 as remainder in each case.

Answer 2

Answer:

The least natural number when divided by 112, 140 and 168 leaves 5 is 1685.

Step-by-step explanation:

Given the numbers 112, 140 and 168.

The smallest number that is exactly divisible by the given numbers must be the least common multiple(LCM) of the given numbers.

The prime factorization of 112: $2 \times 2 \times 2 \times 2 \times 7~ \mbox{or}~ 2^4 \times 7$  or .

The prime factorization of 140: $2 \times 2 \times 5 \times 7~ \mbox{or}~ 2^2 \times 5\times 7$  

The prime factorization of 168: $2 \times 2 \times2 \times 3 \times 7~ \mbox{or}~ 2^3 \times 3\times 7$  

Thus the LCM of 112, 140 and 168 is the product of the common and uncommon prime factors with the greatest exponent.

$2^4 \times 3\times 5\times 7=1680$

Given the number when divided by 112, 140 and 168 leaves 5, therefore, $1680 + 5 = 1685$

Therefore, the least natural number when divided by 112, 140 and 168 leaves 5 is 1685.

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