Find the least number which when divided by:a. 20,24 and 32 leaves 5 a

1.	Find the least number which when divided by:a. 20,24 and 32 leaves 5 as remainder.
Answer» Answer: Now N, when divided by 24, 32 & 42 leaves remainder 5. In other words, (N-5) will be complely divisible by 24, 32 and 42 and the LEAST as well. So, (N-5) has to be the LCM of 24, 32 & 42. LCM (24, 32, 42) = 672 = (N-5) So, N = 677 (Answer) Note: In general, if we have multiple DIVISORS giving the same Remainder, then the number is GIVEN as: [N = LCM of Divisors + Remainder]

Find the least number which when divided by:a. 20,24 and 32 leaves 5 as remainder.

Answer»

Answer:

Now N, when divided by 24, 32 & 42 leaves remainder 5.

In other words, (N-5) will be complely divisible by 24, 32 and 42 and the LEAST as well.

So, (N-5) has to be the LCM of 24, 32 & 42.

LCM (24, 32, 42) = 672 = (N-5)

So, N = 677 (Answer)

Note: In general, if we have multiple DIVISORS giving the same Remainder, then the number is GIVEN as:

[N = LCM of Divisors + Remainder]