Find the smallest number which is divisible by both 644 and 462

English
1

find the smallest number which is divisible by both 644 and 462

2

Find the smallest number which is divisible by both 644 and 462

Answer:
To determine the smallest number that is divisible by both 644 and 462, we calculate the Least Common Multiple (LCM) of these two numbers. The LCM is found by first expressing each number in its prime factorized form and then taking the highest power of each prime that appears in either factorization.

  1. Prime Factorization

    • 644 = 2^2 \times 7 \times 23
    • 462 = 2 \times 3 \times 7 \times 11

  2. Determine the LCM
    Combine each prime factor at its highest power:

    \text{LCM}(644, 462) = 2^2 \times 3^1 \times 7^1 \times 11^1 \times 23^1

  3. Calculate the Product

    • 2^2 = 4
    • 4 \times 3 = 12
    • 12 \times 7 = 84
    • 84 \times 11 = 924
    • 924 \times 23 = 21252

Thus, the smallest number divisible by 644 and 462 is 21252.

Number Prime Factorization LCM Components
644 2^2 \times 7 \times 23 2^2, 7, 23
462 2 \times 3 \times 7 \times 11 2, 3, 7, 11
LCM 2^2 \times 3 \times 7 \times 11 \times 23 21252

@Dersnotu