Find the smallest number which when divided by 28 and 32 leaves remainders 8 and 12 respectively.
Subtract the remainders from the given numbers:
If you look at the negative remainders -
Remainder from 28 = 28 - 8 is - 20.
Remainder from 32 = 32 - 12 is - 20
Find the LCM of the numbers (the least number which all the given numbers divide)
Prime factorization of numbers -
28 = 2 × 2 × 7
32 = 2 × 2 × 2 × 2 × 2
LCM of given numbers = product of prime factors with highest powers = 25 × 7 = 224.
Smallest no, which leaves remainder 8 and 12 when divided by 28 and 32
= LCM - 20 = 224 - 20 = 204