Question

common factor of 680 510 340​

Answer 1

Answer:

. Decompose all numbers into prime factors

510 2 255 3 85 5 17 17 1 680 2 340 2 170 2 85 5 17 17 1

2. Write all numbers as the product of its prime factors

Prime factors of 510 = 2 . 3 . 5 . 17

Prime factors of 680 = 23 . 5 . 17

3. Choose the common and uncommon prime factors with the greatest exponent

Common prime factors: 2 , 5 , 17

Common prime factors with the greatest exponent: 23, 51, 171

Uncommon prime factors: 3

Uncommon prime factors with the greatest exponent: 31

4. Calculate the Least Common Multiple or LCM

Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.

LCM = 23. 51. 171. 31 = 2040

Answer 2

$680 = 2 \times 2 \times 2 \times 5 \times 17 \\ 510 = 2 \times 3 \times 5 \times 17 \\ 340 = 2 \times 2 \times 5 \times 17$

Here,

• Common Factors of 680, 510, and 340 → 2, 5, 17

Therefore,

$LCM = 2 \times 5 \times 17 = \pink{170}$