209 LearnersLast updated on May 26th, 2025
LCM of 5 and 20
LCM is a common multiple, the smallest value between the numbers 5 and 20. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music.
What is the LCM of 5 and 20?
The LCM of 5 and 20 is 20. We can find the LCM using the Listing multiples method, the prime factorization method and the long division method. These are explained below.
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LCM of 5 and 20 Using Listing the Multiples
Step 1: Write down the multiples of the numbers. Don’t stop too early.
Multiples of 5 = 5,10,15,20,25,…
Multiples of 20 = 20,40,60,80…
Step 2: Find the smallest number common between the written multiples of 5 and 20
The smallest common multiple is 20
Thus, LCM(5,20) = 20
LCM of 5 and 20 Using Prime Factorization
Step 1: factorize the numbers into its prime factors
5 = 5
20 = 2×2×5
Step 2: find the highest powers of the factors of 5 and 20
Step 3: Multiply the highest powers
LCM(5,20) = 20
LCM of 5 and 20 Using Division Method
- Write the numbers 5,20 in a row
- Divide them by their common prime factors, if there is one
- Carry forward the numbers that are left undivided by the previously chosen factor
- Continue dividing until the remainder is ‘1’
- Multiply the divisors to find the LCM
- LCM(5,20) = 20
Common Mistakes and how to avoid them while finding the LCM of 5 and 20
Listed here are a few mistakes that one can commit when trying to find the LCM of the numbers 5 and 20. Try to avoid them.
Mistake 1
Listing incorrect multiples
If the LCM of given numbers is 20, double-check that the number appears on the list of both 5 and 20.
Mistake 2
Prime factorization errors
Check if the numbers are prime factored correctly. For example, we may accidentally write 20 = 2×2 instead of 20= 2×2×5
Mistake 3
Thinking product is the LCM
One may think the product of the numbers is the LCM of the numbers. This is only true in case of co-prime numbers.
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LCM of 5 and 20 Examples
Problem 1
Callie and Dan meet every 5 days and 20 days, respectively. They meet today, September 1, how many days will it be before they meet again?
Find the LCM of 5 and 20: LCM (5,20) = 20.
Explanation
They will meet again in 20 days. The LCM of 5 and 20 is the smallest common multiple of the digits.
Problem 2
Ascertain the smallest positive integer solution x to the equation given below, using the LCM of 5 and 20. x=0 (mod 5) and x=0 (mod 20)
Find the prime factors of the numbers:
Prime factorization of 5 = 2
Prime factorization of 20 = 2×2×5
— Take the highest power of each prime factor:
— 2,2,5
— Multiply the ascertained factors to get the LCM:
LCM (5,12) = 2×2×5 = 20
x = 20
Explanation
The question asks to find the smallest x that is divisible by both 5 and 20, which essentially is just finding the least common multiple(LCM) of 5 and 20.
Problem 3
If an integer x is divisible by 5 and 20, express x as a multiple of LCM of 5 and 20. Also, find x.
x is divisible by both 5 and 20, so is must be a multiple of the LCM of the numbers.
LCM that was previously calculated is 20.
Therefore, x = 20.n, for some integer n.
Explanation
The minimum value of x is ascertained when n=1, so the minimum value of x = 20.
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FAQ’s on the LCM of 5 and 20
1.What is the LCM of 5,12 and 15?
2.What is the HCF of 12 and 15?
3.What is the LCM of 15 and 21?
4.What is the LCM of 48 and 60?
5.What is the LCM of 9 and 33?
6.How can children in United States use numbers in everyday life to understand LCM of 5 and 20?
7.What are some fun ways kids in United States can practice LCM of 5 and 20 with numbers?
8.What role do numbers and LCM of 5 and 20 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve LCM of 5 and 20 skills?
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Important glossaries on the LCM of 5 and 20
- Multiple — product of a number and a natural integer
- Prime factor — number one gets after prime factorization any given number
- Prime factorization — the process of breaking the number into its prime factors.
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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.
