Question

Помогите! с решением! НОК(15 И 25) НОК(48 И 42) НОК(56 И 63) НОК (40 И 8) НОК(33 И 3) НОК(16 И 48) С РЕШЕНИЕМ!!!!!!!!24 БАЛЛА!!!!!!

Answer 1

1) НОК(15 И 25)
15=3*5
25=5*5
НОК=3*5*5=75(т. к 5 повторяется и  у 15 и у 25 пишем 1 раз ее)
НОК(15 И 25)=75
2)НОК(48 И 42)
48=2*2*2*2*3
42=2*7*3
НОК=2*2*2*2*3*7=336(т. к 2*3 повторяется и  у 48 и у 42 пишем 1 раз ее)
НОК(48 И 42)=336
3)НОК(56 И 63)
56=2*2*2*7
63=3*3*7
НОК=2*2*2*7*3*3=504(т. к 7 повторяется и  у 56 и у 63 пишем 1 раз ее)
НОК(56 И 63)=504
4) НОК (40 И 8)
40=2*2*2*5
8=2*2*2*2
НОК=2*2*2*5*2=40 (т. к 2*2*2 повторяется и  у 40 и у 8 пишем 1 раз ее)
НОК (40 И 8)=40
5)НОК(33 И 3)
33=3*11
3=3*1
НОК=3*11=33 (т. к 3 повторяется и  у 33 и у 3 пишем 1 раз ее)
НОК(33 И 3)=33
6)НОК(16 И 48)
16=2*2*2*2
48=2*2*2*2*3
НОК=2*2*2*2*3 (т. к 2*2*2*2 повторяется и  у 16 и у 48 пишем 1 раз ее)
НОК(16 И 48)=48

Answer 2

(15 и 25)=5; (48 и 42)=6; (56 и 63)=7; (40 и 8)=8; (33 и 3)=3; (16 и 48)=16

Answer 3

Finding 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 method of finding the LCM of two numbers at a time. Let's use the latter method.

The LCM of two numbers can be found by dividing their product by their greatest common divisor (GCD). We can repeat this process for all pairs of numbers until we find the LCM of all the given numbers.

Let's calculate the LCM step by step:

1. LCM(15, 25): - The product of 15 and 25 is 375. - The GCD of 15 and 25 is 5. - LCM(15, 25) = (15 * 25) / 5 = 75.

2. LCM(48, 42): - The product of 48 and 42 is 2016. - The GCD of 48 and 42 is 6. - LCM(48, 42) = (48 * 42) / 6 = 336.

3. LCM(56, 63): - The product of 56 and 63 is 3528. - The GCD of 56 and 63 is 7. - LCM(56, 63) = (56 * 63) / 7 = 504.

4. LCM(40, 8): - The product of 40 and 8 is 320. - The GCD of 40 and 8 is 8. - LCM(40, 8) = (40 * 8) / 8 = 40.

5. LCM(33, 3): - The product of 33 and 3 is 99. - The GCD of 33 and 3 is 3. - LCM(33, 3) = (33 * 3) / 3 = 33.

6. LCM(16, 48): - The product of 16 and 48 is 768. - The GCD of 16 and 48 is 16. - LCM(16, 48) = (16 * 48) / 16 = 48.

Now, let's find the LCM of the results obtained above:

LCM(75, 336, 504, 40, 33, 48):

- The product of 75, 336, 504, 40, 33, and 48 is 1,027,315,200. - The GCD of 75, 336, 504, 40, 33, and 48 is 1. - LCM(75, 336, 504, 40, 33, 48) = (75 * 336 * 504 * 40 * 33 * 48) / 1 = 1,027,315,200.

Therefore, the least common multiple (LCM) of (15 + I + 25), (48 + I + 42), (56 + I + 63), (40 + I + 8), (33 + I + 3), and (16 + I + 48) is 1,027,315,200.

I hope this helps! Let me know if you have any further questions.