Question

Найти НОК (60 525) НОК (60 315) НОК (270 315) НОК (60 11) НОК ( 270 7) НОК (525 2) НОК (315 3)

Answer 1

Нок
(60 525)-  2100
(60 315) -  1260
(270 315)  - 1890
(60 11)   -660
(270 7)-1890
(525 2)-1050
(315 3)-315

Answer 2

Calculation of the Least Common Multiple (LCM)

To find the least common multiple (LCM) of the given numbers, we can use the prime factorization method or the division method. Let's use the division method to calculate the LCM.

1. LCM(60, 525): - Prime factorization of 60: 2^2 * 3 * 5 - Prime factorization of 525: 3 * 5^2 * 7 - To find the LCM, we take the highest power of each prime factor that appears in either number: LCM(60, 525) = 2^2 * 3 * 5^2 * 7 = 2100

2. LCM(60, 315): - Prime factorization of 60: 2^2 * 3 * 5 - Prime factorization of 315: 3^2 * 5 * 7 - LCM(60, 315) = 2^2 * 3^2 * 5 * 7 = 1260

3. LCM(270, 315): - Prime factorization of 270: 2 * 3^3 * 5 - Prime factorization of 315: 3^2 * 5 * 7 - LCM(270, 315) = 2 * 3^3 * 5 * 7 = 1890

4. LCM(60, 11): - Prime factorization of 60: 2^2 * 3 * 5 - Prime factorization of 11: 11 - LCM(60, 11) = 2^2 * 3 * 5 * 11 = 660

5. LCM(270, 7): - Prime factorization of 270: 2 * 3^3 * 5 - Prime factorization of 7: 7 - LCM(270, 7) = 2 * 3^3 * 5 * 7 = 1890

6. LCM(525, 2): - Prime factorization of 525: 3 * 5^2 * 7 - Prime factorization of 2: 2 - LCM(525, 2) = 2 * 3 * 5^2 * 7 = 2100

7. LCM(315, 3): - Prime factorization of 315: 3^2 * 5 * 7 - Prime factorization of 3: 3 - LCM(315, 3) = 3^2 * 5 * 7 = 315

Now, let's calculate the LCM of the remaining two pairs:

8. LCM(60 + 525, 60 + 315): - LCM(60 + 525, 60 + 315) = LCM(585, 375) = 2925

9. LCM(270 + 315, 60 + 11): - LCM(270 + 315, 60 + 11) = LCM(585, 71) = 41535

Therefore, the calculated LCM values are as follows:

- LCM(60, 525) = 2100 - LCM(60, 315) = 1260 - LCM(270, 315) = 1890 - LCM(60, 11) = 660 - LCM(270, 7) = 1890 - LCM(525, 2) = 2100 - LCM(315, 3) = 315 - LCM(60 + 525, 60 + 315) = 2925 - LCM(270 + 315, 60 + 11) = 41535

Please note that the LCM values calculated above are based on the given numbers and the division method.