248 LearnersLast updated on May 26th, 2025
LCM of 2 and 5
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 2 and 5. 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 2 and 5?
The LCM of 2 and 5 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.
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How to Find the LCM of 2 and 5?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 2 and 5 using the Listing Multiples Method
The LCM of 2 and 5 can be calculated using the following steps:
Steps:
- Write down the multiples of each number
— Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, …
— Multiples of 5 = 5, 10, 15, 20, 25, …
- Ascertain the smallest multiple from the listed multiples
— The smallest common multiple is 10.
Thus, LCM(2, 5) = 10
LCM of 2 and 5 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:
- Find the prime factors of the numbers:
— Prime factorization of 2 = 2
— Prime factorization of 5 = 5
- Take the highest powers of each prime factor:
— Highest power of 2 = 2
— Highest power of 5 = 5
- Multiply the highest powers to get the LCM:
LCM(2, 5) = 2 × 5 = 10.
LCM of 2 and 5 using the Division Method
This method involves dividing the numbers by their common prime factors and multiplying the divisors to obtain the LCM.
Steps:
— Write the numbers, divide by common prime factors and multiply the divisors.
— 2 × 5 = 10
Thus, LCM(2, 5) = 10
Common Mistakes and how to avoid them while finding the LCM of 2 and 5
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 2 and 5 make a note while practicing.
Mistake 1
Listing incorrect/overlooking multiples for the given numbers 2 and 5
This can be avoided by always double-checking the multiples of the numbers 2 and 5 and by not stopping too early. To elaborate, listing 2,4,8 as multiples of 2 and 5,10 as multiples of 5 and assuming 4 is the LCM.
Mistake 2
Confusing between LCM and HCF of the numbers 2 and 5
This can be avoided by learning that the LCM deals with multiples of the numbers 2 and 5, while HCF focuses on divisors of, 2 and 5, i.e., the HCF of 2 and 5 is 1, and the LCM is 10.
Mistake 3
Multiplying the numbers directly
Incorrectly assuming that multiplying the numbers 2 and 5 and assuming the product is the LCM instead of finding the lowest multiple.
Mistake 4
Skipping the LCM in the list method
Oven, the first common multiples in the list of multiples are ignored due to an oversight, like 10 that appears on the list of both 2 and 5.
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LCM of 2 and 5 Examples
Problem 1
The blue tap fills a bucket 2 minutes, and the red tap fills every 5 minutes. How long will it take for both the taps to fill a bucket simultaneously?
The LCM of 2 and 5 is 10.
Explanation
Both the taps will begin filling simultaneously in 10 minutes. The LCM of 2 and 5 is 10, which represents the smallest time interval between the given digits.
Problem 2
The traffic light on the left side changes every 2 minutes and the light on the right side changes every 5 minutes. If both turn green at the same time, how long will it take until they turn green together?
The LCM of 2 and 5 is 10.
Explanation
Both the lights will turn green in 10 minutes, the LCM of 2 and 5. The LCM of 2 and 5 is 10, which represents the smallest time interval between the given digits.
Problem 3
Miss. A assigns math homework to 5th graders every 2 days and science homework to 6th graders every 5 days. If both the grades get their homework today, when will they both receive homework on the same day?
The LCM of 2 and 5 is 10
Explanation
The students will receive homework together again in 10 days. The LCM of 2 and 5 is 10, which represents the smallest time interval between the given digits.
Problem 4
A maintenance schedule for projectors is set up every 2 weeks and 5 weeks at a school. If both the projectors are serviced today, in how many weeks will they be serviced again on the same day?
The LCM of 2 and 5 is 10.
Explanation
Both projectors will need maintenance again in 10 weeks. The LCM of 2 and 5 is 10, which represents the smallest time interval between the given digits.
Problem 5
Two clocks strike every 2 hours and 5 hours. If both of them strike now, when will they next strike together?
The LCM of 2 and 5 is 10.
Explanation
Both clocks will chime together again in 10 hours. The LCM of 2 and 5 is 10, which represents the smallest time interval between the given digits.
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FAQs on LCM of 2 and 5
1.Why is the LCM of 2 and 5 not simply their product (2 × 5 = 10)?
2.What is the LCM formula using the HCF?
3. Is the LCM of numbers 2 and 5 unique? If yes, why?
4.How do you find the LCM of algebraic expressions?
5.How do you derive the LCM of two decimal numbers? Explain using 2 and 5
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Important glossaries for the LCM of 2 and 5
- Prime Factor: A natural number (other than 1) that has factors that are one and itself.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.
- Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.
- 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
: She loves to read number jokes and games.
