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Last updated on December 2nd, 2024

LCM of 2 and 5

Q: Why is the LCM of 2 and 5 not simply their product (2 × 5 = 10)?

Multiplying gives you the product of the numbers, in this case,10. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method.

Q: What is the LCM formula using the HCF?

The LCM can be found using the formula, and as explained with the example given below. LCM (a, b)= a×b/HCF(a, b) For 2 and 5, HCF(2,5)= 1 So, LCM(2,5)=2×5/1 = 1

Q: Is the LCM of numbers 2 and 5 unique? If yes, why?

The LCM of numbers 2 and 5 is unique as it represents the smallest number that both the numbers can divide into with no reminders left behind. To further elaborate; 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. When you divide the LCM with the respective digits; the reminder is ‘0’

Q: How do you find the LCM of algebraic expressions?

For algebraic expressions, find the LCM by factoring each expression and then choosing the highest power of each variable. For example, Find the LCM of x2y and xy3 Factor each term as follows x2y = x2 × y —---> highest power = x2 xy3 = x × y3 —---> highest power = y3 Multiply the highest powers —---> x2y3 LCM(x2y, xy3) = x2y3

Q: How do you derive the LCM of two decimal numbers? Explain using 2 and 5

To derive the LCM of two decimal numbers, follow the below steps; First, convert the given decimals to whole numbers. In the given case, 2.0 and 5.0 are already whole. However, if there is a case where the decimal is, say, 4.5, multiply it by 10 to convert them to a whole number, which will be 45. After converting them into whole numbers, ascertain the LCM of the digits using any of the methods, i.e., the listing multiples method, the division method or the prime factorization method. The LCM (2,5)= 10.

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

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

Ray, the Character from BrightChamps Explaining Math Concepts

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?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

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.