Find the smallest number which when divided by 28 and 32

General
1

find the smallest number which when divided by 28 and 32

2

Find the smallest number which when divided by 28 and 32

Answer: To find the smallest number which, when divided by 28 and 32, gives a remainder of zero, we need to determine the Least Common Multiple (LCM) of the two numbers.

  1. Find the Prime Factorizations of 28 and 32:

    • Prime factorization of 28:

      28 = 2^2 \times 7

    • Prime factorization of 32:

      32 = 2^5

  2. Determine the LCM:

    • The LCM is found by taking the highest power of each prime number that appears in the factorizations.
    • The prime factors are 2 and 7.
    • The highest power of 2 in the factorizations is 2^5 (from 32).
    • The highest power of 7 in the factorizations is 7^1 (from 28).

    Therefore, the LCM is:

    \text{LCM} = 2^5 \times 7^1 = 32 \times 7 = 224

  3. Conclusion:

    • The smallest number which, when divided by both 28 and 32, gives a remainder of zero is 224.

Therefore, the smallest number which when divided by 28 and 32 is exactly divisible by both is \boxed{224}.