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163 LearnersLast updated on December 2nd, 2024
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.
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
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?
Explanation
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?
Explanation
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?
Explanation
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?
Explanation
Problem 5
Two clocks strike every 2 hours and 5 hours. If both of them strike now, when will they next strike together?
Explanation
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
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.
