318 LearnersLast updated on May 26th, 2025
LCM of 4 and 10
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 4 and 10. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.
What is the LCM of 4 and 10?
The LCM of 4 and 10 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations like addition and subtraction with fractions to equate the denominators.
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How to find the LCM of 4 and 10?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 4 and 10 using the Listing Multiples Method
The LCM of 8 and 10 can be found using the following steps:
Steps:
1. Write down the multiples of each number
Multiples of 4 = 4, 8, 12, 16, 20, 24, …
Multiples of 10 = 10, 20, 30, 40, …
2. Ascertain the smallest multiple from the listed multiples
The smallest common multiple is 20. Thus, LCM(4, 10) = 20.
LCM of 4 and 10 using the Prime Factorization Method
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Steps:
1. Find the prime factors of each number:
Prime factorization of 4 = 2×2
Prime factorization of 10 =2×5
2. Take the highest powers of each prime factor and multiply the highest powers to get the LCM:
LCM(4, 10) = 2×2×5= 20
LCM of 4 and 10 using the Division Method
This method involves dividing both numbers by their common prime factors until no further division is possible, and then multiplying the divisors to find the LCM.
Steps:
1. Write the numbers:
2. Divide by common prime factors
3. Multiply the divisors
So, LCM(4, 10) = 20
Common Mistakes and how to avoid them while finding the LCM of 4 and 10
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 4 and 10 make a note while practicing.
Mistake 1
Listing incorrect/overlooking multiples for the given numbers 4 and 10
This can be avoided by always double-checking the multiples of the numbers 4 and 10, and by not stopping too early. To elaborate, listing 4,8,12,16 as multiples of 4 and 10,20,30 as factors of 10 and assuming 12 is the LCM.
Mistake 2
Confusing between LCM and HCF of the numbers 4 and 10
This can be avoided by learning that the LCM deals with multiples of the numbers 4 and 10, while HCF focuses on divisors of 4 and 10, i.e., the HCF of 4 and 10 is 2, and the LCM is 20.
Mistake 3
Skipping the prime factors of the given numbers
Errors in prime factorization often include incorrectly factoring 4 and 10. To illustrate, factoring 10 as 25 instead of 2×5, doing so will yield the wrong LCM.
Mistake 4
Multiplying the numbers directly
Incorrectly assuming that multiplying the numbers 4 and 10 and assuming the product is the LCM instead of finding the lowest multiple.
Mistake 5
Skipping the LCM in the list method
Often, the first common multiples in the list of multiples are ignored due to an oversight, like 20 that appears on the list of both 4 and 10.
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LCM of 4 and 10 Examples
Problem 1
Buses A and B run every 4 days and 10 days respectively. In how many days will they run together again?
LCM(4,10) = 20
Explanation
Both buses will leave the station again on the same day in 20 days, as the LCM of 4 and 10 is 20, which is the smallest time interval between the digits.
Problem 2
A company has meetings every 4 days and 10 days. If both the conference rooms are booked today, when will they next be booked together ?
LCM(4,10) = 20
Explanation
The conference rooms will be booked on the same day in 20 days again, as the LCM of 4 and 10 is 20, which is the smallest time interval between the digits.
Problem 3
Warehouse XYZ restocks sugar every 4 days and pulses every 10 days. If both the goods are restocked today, when will they next be restocked?
LCM(4,10) = 20
Explanation
Sugar and pulses will be restocked in 20 days, the LCM of 4 and 10 is 20, as the LCM of 4 and 10 is 20, which is the smallest time interval between the digits.
Problem 4
The sprinkler watering system waters every 4 days and the drip watering system waters every 10 days. On which day do they have to be turned on together?
LCM(4,10) = 20
Explanation
Both the watering systems have to be turned on together in 20 days, as the LCM of 4 and 10 is 20, which is the smallest time interval between the digits.
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FAQs on LCM of 4 and 10
1.How do you derive the LCM of two decimal numbers? Explain using 4.0 and 10.0?
2.What is the LCM formula using the HCF?
3.Why is the LCM of 4 and 10 not simply their product (4 × 10 = 40) ?
4.How can children in United Kingdom use numbers in everyday life to understand LCM of 4 and 10?
5.What are some fun ways kids in United Kingdom can practice LCM of 4 and 10 with numbers?
6.What role do numbers and LCM of 4 and 10 play in helping children in United Kingdom develop problem-solving skills?
7.How can families in United Kingdom create number-rich environments to improve LCM of 4 and 10 skills?
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Important glossaries for LCM of 4 and 10
- Multiple: A number multiplied with an integer.
- Prime Factor: A natural number (other than 1) whose factors that are one and itself.
- Prime Factorization: Breaking down a number into its prime factors is called Prime Factorization.
- Relatively Prime Numbers: Numbers that have no common factors other than 1.
- Fraction: A representation of a part of a whole.
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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
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