find the smallest number that has factors 3, 9, 14, 45 and 49

Question

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TheRealAera TheRealAera · Answer 1 · 2024-03-05T08:59:27+01:00

Answer:

4410

Step-by-step explanation:

Here, we are looking for least common multiple.

3 and 9 is are factors of 45 so we can also discard them from the beginning.

Now, we are finding the LCM between 14, 45, and 49. We can use prime factorization:

[tex]14=2*7\\45=3*3*5\\49 = 7*7[/tex]

2 occurs once among all 3 numbers

3 occurs twice among all 3 numbers

5 occurs once among all 3 numbers

7 occurs once in 14, but twice in 49, so we use twice for finding LCM.

Thus, the LCM is 2 x 3 x 3 x 5 x 7 x 7 = 4410

rvkacademic rvkacademic · Answer 2 · 2024-03-05T09:05:03+01:00

Answer:

4410

Step-by-step explanation

The question is essentially asking to find the Least Common Multiple (LCM) of 3, 9, 14 and 49

To find LCM

1. List all prime factors for each number.

Prime factorizations of each number:
3 = 3 is prime
9 = 3 x 3
14 = 2 x 7
45 = 3 x 3 x 5
49 = 7 x 7

2. For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
This gives 2, 3, 3, 5, 7, 7

3. Multiply these together to get the LCM
LCM = 2 x 3 x 3 x 5 x 7 x 7 = 4410