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

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.

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 _____
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 ____
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 ____
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 ____
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 ____
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 ____
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 ____
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 ____
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 ____
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 ____
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 ____
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 ___
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 ____
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 ____
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?
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?
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.

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.
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?
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 _____
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 ____
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 ____
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?

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.
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.

Vocabulary Check

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 _____
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.
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