159 LearnersLast updated on May 26th, 2025
LCM of 2,4 and 5
The smallest positive integer that divides the numbers with no numbers left behind is the LCM of 2,4 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 2,4 and 5.
What is the LCM of 2,4 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 2,4 and 5 using listing multiples method
Step 1: List the multiples of each of the numbers;
2 = 2,4,6,8,10,12,14,16,18,20,…
4= 4,8,12,16,20,…
5= 5,10,15,20,…
Step 2: Find the smallest number in both the lists
LCM (2,4,5) = 20
LCM of 2,4 and 5 using prime factorization method
- Prime factorize the numbers
2 = 2
4 = 2×2
5 = 5
- find highest powers
- Multiply the highest powers of the numbers
LCM(2,4,5) = 20
LCM of 2,4 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 (2,4,5) = 20
Common mistakes and how to avoid them in LCM of 2,4 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 2,4 and 5 Examples
Problem 1
A number is divisible by 4 and 5, and also by 2. Find the missing number if the LCM of 2, 4, and the missing number is 20.
Since LCM(2, 4, x) = 20,
we know x must be a divisor of 20. The prime factorization of 20 is 22×5, so x must include a factor of 5. Thus, the missing number is 5.
Explanation
The LCM of any number that already includes the factors of 2 and 4 would need an additional factor of 5 to make 20, leading to x = 5.
Problem 2
Find the smallest number divisible by 2, 4, and 5 that leaves a remainder of 1 when divided by 3.
The LCM of 2, 4, and 5 is 20.
Now, find the smallest multiple of 20 that leaves a remainder of 1 when divided by 3.
20÷3=6 remainder 2,
so the next multiple to check is 20 + 1 = 21.
Therefore, the smallest number divisible by 2, 4, and 5 that leaves a remainder of 1 when divided by 3 is 21.
Explanation
The LCM ensures divisibility by 2, 4, and 5. We then search for the smallest number of the form 20k + 1 that satisfies the remainder condition.
Problem 3
Compare the LCM of 2, 4, and 5 with the LCM of 3, 6, and 9. Which is larger?
LCM(2, 4, 5) = 20
LCM(3, 6, 9):
Prime factorization;
3 = 3
6 = 2 × 3
9 = 3²
LCM(3, 6, 9) = 2 × 3² = 18
Therefore, LCM(2, 4, 5) = 20 is larger than LCM(3, 6, 9) = 18.
Explanation
This problem demonstrates how the LCM can be used to compare sets of numbers with different prime factorizations.
FAQs on the LCM of 2,4 and 5
1.What is the LCM of 2,3 and 4?
2.What is the LCM of 3 and 9?
3. What is the LCM of 7 and 8?
4. What is the LCM of 4 and 7?
5.What is the LCM of 8 and 9?
6.How can children in United Kingdom use numbers in everyday life to understand LCM of 2,4 and 5 ?
7.What are some fun ways kids in United Kingdom can practice LCM of 2,4 and 5 with numbers?
8.What role do numbers and LCM of 2,4 and 5 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve LCM of 2,4 and 5 skills?
Important glossaries for LCM of 2,4 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.
