LCM&GCF

Question 1

How do you find LCM

Answer 1

Find the prime factors of the numbers, list the highest powers of each prime factor, and multiply them to get the LCM.

Question 2

How do you find GCF

Answer 2

Find the prime factors of the numbers, identify the common prime factors, and multiply them to get the GCF.

Question 3

Which of the following is the LCM of 30 and 22

330
23
2
1

Answer 3

330 is the LCM:
Prime factors of 30: 2 × 3 × 5.

Prime factors of 22: 2 × 11.

To find the LCM, list the highest power of each prime factor that appears in either number.

LCM(30, 22) = 2 × 3 × 5 × 11 = 330.

Question 4

Which of the following is the GCF of 225 and 165
7425
380
15
5

Answer 4

5 is the GCF:
Prime factors of 225: 3 × 3 × 5 × 5 (or 3^2 × 5^2).

Prime factors of 165: 3 × 5 × 11.

Identify the common prime factors.

GCF(225, 165) = 3 × 5 = 15.

Question 5

Ayetil has 21 scarves and Isla has 49 scarves. What is the largest number of scarves they can deliver in a box if they have to give the same amount of scarves in their boxes?

Answer 5

Prime factors of 21: 3 × 7.

Prime factors of 49: 7 × 7 (or 7^2).

The common prime factor is 7.

So, they can deliver 7 scarves in each box, which is the GCF of 21 and 49.

Question 6

Solas has 32 cat shoes and Max has 80. What is the largest number of shoes they can deliver in a box if they have to give the same amount of shoes in their boxes?

Answer 6

Prime factors of 32: 2 × 2 × 2 × 2 × 2 (or 2^5).
Prime factors of 80: 2 × 2 × 2 × 2 × 5 (or 2^4 × 5).The common prime factor is 2, and it appears five times in 32 and four times in 80.
So, the largest number of shoes they can deliver in a box is 2^4, which is 16. 16 is the GCF.

Question 7

Mr Daisern is planning to go to the club with Ms Cheienne. He is vailiable every 14 days and she is availiable every 21. After how many days can he take her to the club?

Answer 7

The prime factors of 14 are 2 and 7.

The prime factors of 21 are 3 and 7.

Now, multiply all the unique prime factors together: 2 × 3 × 7 = 42.

So, the LCM of 14 and 21 is 42, which means they will go to the club together every 42 days.

Question 8

Daabil wants to go to the park with Aitif. Aitif is available every 15 days. Daabil is available every 65 days.When will they go?

Answer 8

Prime factors of 15: 3 × 5

Prime factors of 65: 5 × 13

Now, find the LCM by multiplying the highest power of each unique prime factor:

LCM(15, 65) = 3 × 5 × 13 = 195

They will meet after 195 days

Question 9

LCM or GCF

24:2x2x2x3
78:2x3x13
(2x2x2)x3x13=312

Answer 9

LCM

Question 10

LCM or GCF
24:2x2x2x3
36:2x2x3x3
2x2x2x3x3=72

Answer 10

LCM

Question 11

LCM or GCF
20:2x2x5
112:2x2x2x2x7
2x2=4

Answer 11

GCF

Question 12

LCM or GCF
3x3x5=45
3x3x3x3=81
3x3=9

Answer 12

GCF