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170 LearnersLast updated on November 29th, 2024
LCM of 3,4 and 5
The smallest positive integer that divides the numbers with no numbers left behind is the LCM of 3,4 and 5. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music. In this article, let’s now learn to find LCMs of 3,4 and 5.
What is LCM of 3,4 and 5
We can find the LCM using listing multiples method, prime factorization method and the long division method. These methods are explained here, apply a method that fits your understanding well.
LCM of 3,4 and 5 using listing multiples method
Step 1: List the multiples of each of the numbers;
3 =3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,…60
4= 4,8,12,16,20,…60
5= 5,10,15,20,…60
Step 2:Find the smallest number in both the lists
LCM (3,4,5) = 60
LCM of 3,4 and 5 using prime factorization method
Step 1: Prime factorize the numbers
3 = 3
4 = 2×2
5 = 5
Step 2: find highest powers
Step 3: Multiply the highest powers of the numbers
LCM(3,4,5) = 60
LCM of 3,4 and 5 using division method
- Write the numbers in a row
- Divide them with a common prime factor
- Carry forward numbers that are left undivided
- Continue dividing until the remainder is ‘1’
- Multiply the divisors to find the LCM
- LCM (3,4,5) = 60
Common mistakes and how to avoid them in LCM of 3,4 and 5
LCM of 3,4 and 5 Examples
Problem 1
A number is divisible by both 3 and 4 but not divisible by 5. If the LCM of 3, 4, and another number is 60, what is the missing number?
Explanation
Problem 2
If n=LCM(3,4,5), find the number of divisors of n.
Explanation
Problem 3
If the GCF of two numbers is 1 and their LCM is 60, what can you say about the numbers if one of them is 4?
Explanation
FAQs on the LCM of 3,4 and 5
1.What is the LCM of 2,3 and 4?
2.What are the factors of 3,4, and 5?
3. What is the LCM of 4 and 7?
4.What is the GCF of 17 and 19?
Important glossaries for LCM of 3,4 and 5
- Multiple: the result after multiplication of a number and an integer. To explain, 5×5 =25; 25 is a multiple of 5.
- Prime Factor: A number with only two factors, 1 and the number. For example,7, its factors are only 1 and 7 and the number when divided by any other integer will leave a remainder behind.
- Prime Factorization: breaking a number down into its prime factors. For example, 60 is written as the product of 2×2×3×5.
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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.
