How do you find the least common multiple in 5th grade?

The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. To find the LCM, you can list the multiples of each number and find the smallest one they share, or use prime factorization to break down the numbers into their prime factors and multiply the highest powers of each factor.

What is the Lowest Common Multiple lesson note?

The lowest common multiple is the lowest multiple shared by two or more numbers . For example, common multiples of 4 and 6 are 12, 24 and 36, but the lowest of those is 12; therefore, the lowest common multiple of 4 and 6 is 12.

How to find LCM for 5?

The LCM of 5 and 5 is 5. To find the LCM of 5 and 5, we need to find the multiples of 5(multiples of 5 = 5, 10, 15, 20, . .) and choose the smallest multiple that is exactly divisible by 5 and 5, i.e., 5 .

What are 5 multiples of 8?

The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 … and so on. It is a sequence where the difference between each next number and the preceding number, i.e. two consecutive results, is 8.

Do 5 and 8 have common factors?

The GCF of 5 and 8 is 1 . To calculate the greatest common factor (GCF) of 5 and 8, we need to factor each number (factors of 5 = 1, 5; factors of 8 = 1, 2, 4, 8) and choose the greatest factor that exactly divides both 5 and 8, i.e., 1.

How to check if LCM is correct?

LCM by Listing Method Step 1: List the first few multiples of A and B. Step 2: Mark the common multiples from the multiples of both numbers. Step 3: Select the smallest common multiple. That lowest common multiple is the LCM of the two numbers.

Here's how to find the GCF of a set of numbers using prime factorization: List the prime factors of each number. Circle every common prime factor — that is, every prime factor that's a factor of every number in the set. Multiply all the circled numbers. The result is the GCF. Jul 9, 2021

What is the answer of least common multiple?

For two integers a and b, denoted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b . For example, LCM(2,3) = 6 and LCM(6,10) = 30. The LCM of two or more numbers is the smallest number that is evenly divisible by all numbers in the set.

What is LCM with an example?

LCM is the smallest integer which is a multiple of two or more numbers. For example, LCM of 4 and 6 is 12, and LCM of 10 and 15 is 30. As with the greatest common divisors, there are many methods for computing the least common multiples also. One method is to factor both numbers into their primes.

What is the LCM of 12 and 18?

What is LCM of 12 and 18. The Least Common Multiple or Lowest Common Multiple of 12 and 18 is 36 .

McGraw Hill My Math Grade 5 Chapter 8 Lesson 5 Answer Key Least Common Multiple (2024)

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 8 Lesson 5 Least Common Multiplewill 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 numbersmay be one of the numbers.
Consider three numbers 3 , 4 , 12
Now, LCM of3,4and12is12which 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 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 be15 weeksbecause 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.

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 _____
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.

McGraw Hill My Math Grade 5 Chapter 8 Lesson 5 Answer Key Least Common Multiple (2024)

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

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

FAQs

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References