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8 ಮತ್ತು 1 ಅರಿಂದ ಪೂರ್ಣವಾಗಿ ಆಗುವಾಗು ಕೆಳಗೆ ಬರುವಂಥ ಸಂಖ್ಯೆಗಳಲ್ಲಿ

Mathematics

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Answer

120\text{120}

Step-by-step solution

4 steps

  1. Understand the question.

    The question asks to find the least number that is completely divisible by 6, 8, and 10. This means we need to find the Least Common Multiple (LCM) of these three numbers.

  2. Find the prime factorization of each number.

    6=2×36 = 2 \times 3 8=2×2×2=238 = 2 \times 2 \times 2 = 2^3 10=2×510 = 2 \times 5

  3. Calculate the LCM using the prime factorizations.

    To find the LCM, we take the highest power of each prime factor that appears in any of the factorizations.

    • The highest power of 2 is 232^3 (from the factorization of 8).
    • The highest power of 3 is 313^1 (from the factorization of 6).
    • The highest power of 5 is 515^1 (from the factorization of 10).

  4. Multiply these highest powers together to get the LCM.

    LCM(6,8,10)=23×31×51\text{LCM}(6, 8, 10) = 2^3 \times 3^1 \times 5^1 LCM(6,8,10)=8×3×5\text{LCM}(6, 8, 10) = 8 \times 3 \times 5 LCM(6,8,10)=24×5\text{LCM}(6, 8, 10) = 24 \times 5 LCM(6,8,10)=120\text{LCM}(6, 8, 10) = 120

    The least number completely divisible by 6, 8, and 10 is 120\boxed{\text{120}}.

    Just one more to go today! Send it over.

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