179 LearnersLast updated on May 26th, 2025
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
Listed here are a few mistakes children may make when trying to find the LCM due to confusion or due to unclear understanding. Be mindful, understand, learn and avoid!
Mistake 1
Duplicating or skipping a factor
A factor may be missed when we prime factorize a number. Writing the prime factorization of 4 may be written as 3×2 instead of 2×2 accidentally.
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?
Since the number is divisible by both 3 and 4, its LCM with these numbers must be divisible by their LCM (which is 12).
However, it should not include a factor of 5.
The number that satisfies this condition is 12, since:
LCM(3, 4, 12) = 60.
Explanation
The missing number is 12.
Problem 2
If n=LCM(3,4,5), find the number of divisors of n.
First, find the LCM(3, 4, 5) = 60 (already solved).
Now, find the number of divisors of 60. The prime factorization of 60 is:
60=22×3×5
The number of divisors of a number is given by the formula:
Number of divisors=(e1+1)(e2+1)…(ek+1)
where e1, e2, …, ek are the exponents in the prime factorization.
For 60:
Number of divisors=(2+1)(1+1)(1+1)=3×2×2=12
Explanation
The number of divisors of 60 is 12.
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?
Let the two numbers be 4 and x. We are given:
GCF(4,x)=1 and LCM(4,x)=60
Since GCF(4, x) = 1, x must not share any prime factors with 4 (which has the prime factorization 22).
Thus, x must be divisible by 3 and 5 (since 60=22×3×5, and we already accounted for the 22in 4).
Therefore,
x=15x = 15x=15.
Explanation
The other number is 15.
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?
5.How can children in United States use numbers in everyday life to understand LCM of 3,4 and 5 ?
6.What are some fun ways kids in United States can practice LCM of 3,4 and 5 with numbers?
7.What role do numbers and LCM of 3,4 and 5 play in helping children in United States develop problem-solving skills?
8.How can families in United States create number-rich environments to improve LCM of 3,4 and 5 skills?
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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About BrightChamps in United States
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.
