Question

find the least number which when divided by 7,8, and 12 leaves the same remainder 5 in each case.​

Answer 1

Answer:

Correct option is 505

Step-by-step explanation:

Here we need to find the least number which when divided by 7,8, and 12 leaves the same remainder 5 in each case :

Writing the prime factorization:

       7 = 1 × 7

       8 = 2 × 2 × 2

       9 = 3 × 3

       12 = 2 × 2 × 3

Prime factorization is a process of writing all numbers as a product of primes. So, for example, say if we have something like the number 20. We can break that down into two factors. We can say, “well, that's 4 times 5.” And notice, 5 is a prime number.

the least common multiple therefore is:

       2×7×2×2×3×3=504

So numbers which on being divided by 6,7,8,9 and 12 leave a remainder 1 are : 504+1=505

Hence , the correct answer is 505.

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