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152 LearnersLast updated on December 24th, 2024
LCM of 3, 5 and 7
Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 3, 5, and 7. By learning the following tricks, you can learn the LCM of 3, 5, and 7.
What is the LCM of 3, 5, and 7?
The LCM of 3, 5, and 7 is 105. How did we get 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 3, 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 multiples
Method 2: Prime factorization
Method 3: Division method
Now let us delve further into these three methods and how it benefits us.
LCM OF 3, 5, and 7 Using Listing the Multiplies
In this method, we will list all the multiples of 3, 5, and 7. Then we will try to find a multiple that is present to all the numbers.
For example,
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 105, 108
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105
The LCM of 3, 5, and 7 is 105. 105 is the smallest number which can be divisible by 3, 5, and 7
LCM of 3, 5, and 7 Using prime factorization
To find the LCM of 3, 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 3 are: 31
Prime factors of 5 are: 51
Prime factors of 7 are: 71
Multiply the highest power of both the factors: 31 × 51 × 71 = 3 × 5 × 7=105
Therefore, the LCM of 3, 5, and 7 is 105
LCM of 3, 5, and 7 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 14 and 24 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 3, 5, and 7.
3 × 5 × 7 = 105
The LCM of 3, 5, and 7 is 105.
Common Mistakes and How to Avoid Them in LCM of 3, 5 and 7.
LCM of 3,5 and 7 examples
Problem 1
Check whether 105 is the LCM of 3, 5, and 7.
Explanation
Problem 2
John has swimming class every 3 days, drawing class every 5 days, and math class every 7 days. On which day would all three classes happen on the same day?
Explanation
Problem 3
There are three movies showing in the local cinemas. The first movie plays every 3 hours, the second every 5, and the third every 7 hours. Today all three movies are showing at the same time, so after how many hours will all three movies show at the same time?
Explanation
Problem 4
A bus travels to the mall every 3 hours, another bus travels to the mall every 5 hours. A third bus travels to the same mall every 7 hours. How many hours will it take for all three buses to meet at the same time?
Explanation
Problem 5
There are three lights blinking at different intervals. The first light blinks every 3 seconds, the second light blinks every 5 seconds, and the third blinks every 7 seconds. After how many seconds will they blink together again?
Explanation
FAQs on least common multiple of 3, 5, and 7
1.Calculate the LCM of 3, 5, 5, and 7?
2.How to calculate the LCM of 3, 5, and 6 using the division method?
3.What is the HCF of 3, 5, and 7
Important glossaries for LCM of 3, 5 and 7
- Prime Number: Any number that has only 2 factors is called a prime number.For 5 and 7, 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.
