All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 8 Lesson 5 Least Common Multiple** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 8 Lesson 5 Least Common Multiple

**Math in My World**

Example 1

Tom hits golf balls at the driving range every 3 days, practices putting every 4 days, and goes golfing every 6 days. If he did all three activities today, in how many days will he do all three activities again?

Find and circle the LCM of 3, 4 and 6 by listing nonzero multiples of each number.

3: 3, 6, 9, 12, 15, 18, 21, 24, 27 and 30.

4: 4, 8, 12, 26, 20, 24, 28, 32, 36 and 40.

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.

So, Tom will complete all three activities again in 12 days.

Check The number line shows on which days all three activities will be completed.

Example 2

Find the LCM of 15 and 40.

1. write the prime factorization of each number.

2. Find the common prime factors.

15 = 3 × 5 ← The only common prime factor is 5.

40 = 2 × 2 × 2 × 5

3. Find the product of the prime factors using each common prime factor only once and any remaining factors.

The LCM is 3 × 5 × 2 × 2× 2= 120

**Talk Math**

Could the LCM of two numbers be one of the numbers? Explain.

Answer:

LCM of two or more numbers may be one of the numbers.

Consider three numbers 3 , 4 , 12

Now, LCM of 3,4 and 12 is 12 which is one of the given numbers.

**Guided Practice**

**Find the LCM of each set of numbers.**

Question 1.

6, 10

6: ________

10: _______

So, the LCM of 6 and 10 is _____

Answer:

30

Explanation:

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

10 : 10, 20, 30, 40, 50, 60, 70, 80, 90

So, the LCM of 6 and 10 is 30

Question 2.

3, 4

3: ______

4: _____

So, the LCM of 3 and 4 is ____

Answer:

12

Explanation:

3: 3, 6, 9, 12, 15, 18, 21, 24, 27 and 30.

4: 4, 8, 12, 26, 20, 24, 28, 32, 36 and 40.

So, the LCM of 3 and 4 is 12

**Independent Practice**

**Find the LCM of each set of numbers.**

Question 3.

2, 13 ____

Answer:

26

Explanation:

2 : 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26

13 : 13, 26, 39, 52, 65, 78, 91, 104, 117

So, the LCM of 2 and 13 is 26

Question 4.

7, 9 ____

Answer:

63

Explanation:

7 : 7 ,14 ,21 ,28 ,35 ,42 ,49 ,56 ,63 ,70

9 : 9, 18, 27, 36, 45, 54, 63, 72, 81, 90.

So, the LCM of 7 and 9 is 63

Question 5.

2, 10 ____

Answer:

10

Explanation:

2 : 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

10 : 10, 20, 30, 40, 50, 60, 70, 80, 90

So, the LCM of 2 and 10 is 10

Question 6.

12, 15 ____

Answer:

60

Explanation:

12 : 12, 24, 36, 48, 60, 72, 84, 96

15 : 15, 30, 45, 60, 75, 90, 105, 120, 135

So, the LCM of 12 and 15 is 60

Question 7.

16, 20 ____

Answer:

80

Explanation:

16 : 16, 32, 48, 64, 80, 96, 112, 128

20 : 20, 40, 60, 80, 100, 120, 140, 160, 180

So, the LCM of 16 and 20 is 80

Question 8.

3, 8 ____

Answer:

24

Explanation:

3: 3, 6, 9, 12, 15, 18, 21, 24, 27

8 : 8, 16, 24, 32, 40, 48, 56, 64

So, the LCM of 3 and 8 is 24

Question 9.

4, 8, 10 ____

Answer:

40

Explanation:

4 : 4, 8, 12, 26, 20, 24, 28, 32, 36 and 40

8 : 8, 16, 24, 32, 40, 48, 56, 64

10 : 10, 20, 30, 40, 50, 60, 70, 80, 90

So, the LCM of 4 , 8 and 10 is 40

Question 10.

3, 9, 18 ____

Answer:

18

Explanation:

3: 3, 6, 9, 12, 15, 18, 21, 24, 27

9 : 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

18 : 18, 36, 54, 72, 90, 108, 126

So, the LCM of 3 , 9 and 18 is 18

Question 11.

15, 25, 75 ____

Answer:

75

Explanation:

15 : 15, 30, 45, 60, 75, 90, 105, 120

25 : 25, 50, 75, 100, 125, 150

75: 75, 150, 225, 300

So, the LCM of 15 , 25 and 75 is 75

Question 12.

9, 12, 15 ___

Answer:

180

Explanation:

9 : 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180

12 :12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180

15 :15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180

So, the LCM of 9 , 12 and 15 is 180

Question 13.

4, 7, 10 ____

Answer:

140

Explanation:

4: 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100,104,108,112,116,120,124,128,132,136,140

7: 7,14,21,28,35,42,49,56 ,63,70,77, 84, 91, 98,105,112,119,126,133,140

10 : 10,20,30,40,50,60,70,80,90,100,110,120,130,140,150

So, the LCM of 4, 7and 10 is 140

Question 14.

6, 7, 9 ____

Answer:

126

Explanation:

6 : 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96,102, 108, 114, 120,126

7: 7,14,21,28,35,42,49,56 ,63,70,77, 84, 91, 98,105,112,119,126

9 : 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126

So, the LCM of 6, 7and 9 is 126

**Problem Solving**

Question 15.

Juan goes to the bowling alley every 3 weeks. Percy goes to the bowling alley every 5 weeks. If Juan and Percy meet the first time they go bowling, how many weeks will it be before they see each other at the bowling alley again?

Answer:

The first time Percy and Juan meet will be 15 weeks because it is the common multiple of both 5 and 3.

Explanation:

3: 3, 6, 9, 12, 15, 18, 21, 24, 27

5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

So, the LCM of 3 and 5 is 15

Question 16.

A full moon occurs about every 30 days. If the last full moon occurred on a Friday, how many days will pass before a full moon occurs again on a Friday?

Answer:

210

Explanation:

A full moon occurs every 30 days

A Friday occurs every 7 days

You must find out when those days will occur at the same time.

Simplest answer is 7 x 30 = 210 days

7 : 7,14,21,28,35,42,49,56 ,63,70,77, 84, 91, 98,105,112,119,126,133,140,147,154,161,168,175,182,189,196,203,210

30 : 30, 60,90,120,150,180,210

So, the LCM of 7 and 30 is 210

**HOT Problems**

Question 17.

**Mathematical PRACTICE 3 Find the Error** Maria is finding the LCM of 6 and 8. Help find and correct her mistake.

Answer:

24

Explanation:

The common prime factors of 6 = 2 × 3

The common prime factors of 8 = 2 × 2 × 2

So only common factor is 2 then,

LCM = 2 × 3 × 2× 2 =24

Question 18.

**Mathematical PRACTICE 4 Model Math** Write a real-world problem in which it would be helpful to find the least common multiple.

Answer:

An example would be a scenario where you and your friend are going to a a restaurant.

You have lunch there every fourth day, and he has his lunch there every sixth day.

How many days before you meet again for lunch at the same restaurant?

The answer again is lcm(4, 6) = 12.

Question 19.

**? Building on the Essential Question** How can I find the least common multiple of two or more numbers?

Answer:

The formula to find LCM of two numbers is, LCM of two numbers = product of two numbers ÷ HCF of two numbers or

find all the prime factors of each given number.

List all the prime numbers found, as many times as they occur most often for any one given number.

Multiply the list of prime factors together to find the LCM.

### McGraw Hill My Math Grade 5 Chapter 4 Lesson 5 My Homework Answer Key

**Practice**

**Find the LCM of each set of numbers.**

Question 1.

7, 14 _____

Answer:

14

Explanation:

7 : 7 ,14 ,21 ,28 ,35 ,42 ,49 ,56 ,63 ,70

14 : 14, 28, 42, 56, 70, 84, 98

So, the LCM of 7 and 14 is 14

Question 2.

6, 15 ____

Answer:

30

Explanation:

6 : 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

15 : 15, 30, 45, 60, 75, 90, 105, 120

So, the LCM of 6 and 15 is 30

Question 3.

5, 9, 15 ____

Answer:

45

Explanation:

5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

9 : 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

15 : 15, 30, 45, 60, 75, 90, 105, 120

So, the LCM of 5 , 9 and 15 is 45

**Problem Solving**

Question 4.

The cycles for two different events are shown in the table. Each of these events happened in the year 2000. What is the next year in which both will happen?

Answer:

The next year in which both will happen is 2020

Explanation:

4 : 4, 8, 12, 26, 20, 24, 28, 32, 36 and 40

10 : 10, 20, 30, 40, 50, 60

So, the LCM of 4 and 10 is 20

We can add this value to the year when the events occurred together last , that is 2000 and we get 2000 + 20 = 2020

Question 5.

**Mathematical Practice 3 Draw a Conclusion** Is the statement below always, sometimes, or never true? Give at least two examples to support your reasoning. The LCM of two numbers is the product of the two numbers.

Answer:

Sometimes true

Explanation:

The Least Common Multiple of two numbers is the product of the two numbers only when they are relatively prime.

5, 21 LCM = 105

91, 11 LCM = 1001

If two numbers share a common factor, 8 and 10 share 2 as a common factor,

the least common multiplier of 8 and 10 is 40.

**Fill in each blank with the correct word(s) to complete each sentence.**

Question 6.

Multiples that are shared by two or more numbers are _____

Answer:

Common multiples

Explanation:

Multiples that are shared by two or more numbers are Common multiples

Question 7.

The least common multiple (LCM) is the ____ multiple, other than 0, common to sets of multiples.

Answer:

Least

Explanation:

The least common multiple (LCM) is the least multiple, other than 0, common to sets of multiples.

**Test Practice**

Question 8.

Micah is buying items for a birthday party. If he wants to have the same amount of each item, what is the least number of packages of cups he needs to buy?

A. 2 packages

B. 3 packages

C. 4 packages

D. 5 packages

Answer:

C

Explanation:

Multiples of 6 =6, 12, 18, 24, 30, 36, 42, 48, 54, 60

Multiples of 8 =8, 16, 24, 32, 40, 48, 56, 64, 72

LCM of 6 and 8 is 24

Now we will divide 24 by 6 to find number of packages of cups that Micah needs to purchase.

24/6 = 4

Therefore, Micah needs to by 4 package of cups at least.

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