find the smallest number which leaves remainder 8 and 12 when divided by 28 and 32 respectively
find the smallest number which leaves remainder 8 and 12 when divided by 28 and 32 respectively
Answer :
To find the smallest number that leaves a remainder of 8 when divided by 28 and a remainder of 12 when divided by 32, we need to find the least common multiple (LCM) of 28 and 32. The LCM will be the smallest number that satisfies both conditions.
Prime factorizing 28 and 32:
28 = 2^2 * 7
32 = 2^5
To find the LCM, we take the highest power of each prime factor that appears in either number:
2^5 * 7 = 224
Smallest no: which leaves remainder 8 and 12 when divided by 28 and 32 = LCM -20 = 224 - 20 = 204
204 is the correct answer.