146 LearnersLast updated on May 26th, 2025
LCM of 4,5 and 7
Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 4, 5, and 7. By learning the following tricks, you can learn the LCM of 4, 5, and 7 easily.
What Is the LCM of 4, 5, and 7?
The LCM of 4, 5, and 7 is 140. How did we get to this answer, though? That’s what we’re going to learn. We also see how we can find the LCM of 2 or more numbers in different ways.
How to find the LCM of 4, 5, and 7?
We have already read about how you can approach finding the LCM of 2 or more numbers. Here is a list of those methods which make it easy to find the LCMs:
Method 1: Listing of Multiples
Method 2: Prime Factorization
Method 3: Division Method
Now let us delve further into these three methods and how it benefit us.
LCM of 4, 5, and 7 Using Listing of Multiples Method
In this method, we will list all the multiples of 4, 5, and 7. Then we will try to find a multiple that is present in both numbers.
For example,
Multiples of 4:
4, 8, 12,…..100,104,108,112,116,120,124,128,132,136,140….
Multiples of 5:
5, 10, 15,…..100,105,110,115,120,125,130,135,140….
Multiples of 7:
7, 14, 21,……91,98,105,112,119,126,133,140….
The LCM of 4, 5, and 7 is 140. 140 is the smallest number which can be divisible by 4, 5, and 7.
LCM of 4, 5, and 7 Using Prime Factorization
To find the LCM of 4, 5, and 7 using the prime factorization method, we need to find out the prime factors of both the numbers. Then multiply the highest powers of the factors to get the LCM.
Prime Factors of 4 are: 22
Prime Factors of 5 are: 51
Prime Factors of 7 are: 71.
Multiply the highest powers of both the factors: 22 × 51 × 71 = 2 × 2 × 5 × 7 = 140
Therefore, the LCM of 4, 5 and 7 is 140.
LCM of 4, 5, and 7 Using Division Method
To calculate the LCM using the division method. We will divide the given numbers with their prime numbers. The prime numbers should at least divide any one of the given numbers. Divide the numbers till the remainder becomes 1. By multiplying the prime factors, one can get LCM.
For finding the LCM of 4, 5, and 7 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 4, 5, and 7.
2 × 2 × 5 × 7 = 140
The LCM of 4, 5, and 7 is 140
Common Mistakes and How to Avoid Them in LCM of 4, 5, and 7.
Mistakes are common when we are finding the LCM of numbers. By learning the following common mistakes, we can avoid the mistakes.
Mistake 1
Missing a prime factor
Children sometimes may forget to write all the prime factors for a given number. So, at the start we have to write all the prime factors for the given numbers which won’t cause any problems later on.
LCM of 4, 5, and 7 Examples
Problem 1
Three employees are working on a project. Employee A completes a task every 4 days, Employee B every 5 days, and Employee C every 7 days. After how many days will all three employees complete their tasks on the same day again? What percentage of the total days will Employee A, B, and C be working individually before they all finish on the same day?
We find the LCM of 4, 5, and 7:
Prime factorization of the numbers → 4 = 22, 5 = 51, and 7 = 71
LCM = 22×5×7=140
All three employees will complete their tasks on the same day every 140 days.
Now, calculate the percentage of days each employee works individually within these 140 days:
Employee A: 140 days/4=35 times.
Employee B: 140 days/5=28 times.
Employee C: 140 days/7=20 times.
The percentage of work days for each:
Employee A: 35/140×100 = 25%
Employee B: 28/140×100 = 20%
Employee C: 20/140×100 = 14.29%
Explanation
In this problem, the LCM of 4, 5, and 7 gives the interval at which all employees will finish a task together. By dividing the total days by each employee's interval, we find their individual contribution to the total work period in terms of percentages.
Problem 2
Suppose a bus route passes every 4 minutes, a train every 5 minutes, and a tram every 7 minutes. At 8 AM they arrive. Using the formula for LCM, determine the next time they will all pass by together.
Step 1: Using the LCM formula for 4, 5, and 7, we find the interval at which they align.
LCM of 4, 5, and 7 = 140 minutes.
Step 2:Convert 140 minutes to hours:
140÷60=2 hours and 20 minutes.
Step 3: find the time after which they will pass again
8:00 AM+2 hours 20 minutes = 10:20 AM.
Explanation
This formula-based example uses the LCM to find the common passing time for multiple intervals, then converts it into hours and minutes. This problem highlights the utility of the LCM in synchronizing events occurring at different intervals.
Problem 3
Verify that the LCM of 4, 5, and 7 is consistent with the relationship:LCM=Product of numbers/GCF of numbers. Find the LCM using this.
Step 1: Calculate the product
4×5×7=140
Step 2: Find the Greatest Common Factors (GCF) of 4, 5, and 7:
Since they have no common factors other than 1, GCF = 1.
Step 3: Verify using the relationship:
LCM=4×5×7/1=140
Explanation
This problem verifies the relationship between the LCM, product, and GCF of a set of numbers
FAQs on LCM of 4,6, and 7
1.What is the LCM of 4,6, and 7?
2.What is the LCM of 4,4, and 7?
3. What is the LCM of 4,3,5, and 7?
4.Find GCF of 4,5 and 7.
5. Find the LCM of 4,7 and 10.
6.How can children in India use numbers in everyday life to understand LCM of 4,5 and 7?
7.What are some fun ways kids in India can practice LCM of 4,5 and 7 with numbers?
8.What role do numbers and LCM of 4,5 and 7 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve LCM of 4,5 and 7 skills?
Important glossaries for the LCM of 4,5 and 7
- Prime Number: Any number that has only 2 factors is called a prime number.For example, 5 and 7, the only common factors are 1 and the number itself.
- Composite Number: Any number that has more than 2 factors is called a composite number. For example, 4,8, and 10.
- Prime Factorization: It is breaking down a number into smaller prime numbers, then multiplied together, giving the same number.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
