Find the least natural number which leaves the remainders 6 and 8 when divided by 7 and 9 respectively.

Take L.C.M of 7 and 9.

We get, L.C.M (7, 9) = 7 × 9 [∵ 7 and 9 are co-primes]

⇒ L.C.M (7, 9) = 63

Now, we need to subtract 1 from L.C.M of 7 and 9.

So, 63 – 1 = 62

Dividing 62 by 7,

62 = (7 × 8) + 6

Notice, by dividing 62 by 7, we have got remainder as 6.

Dividing 62 by 9,

62 = (9 × 6) + 8

Notice, by dividing 62 by 9, we have got remainder as 8.

Thus, we can conclude that the least natural number is 62, which leaves the remainder 6 and 8 when divided by 7 and 9 respectively.