Methods to Find the LCM of 2, 3, and 5

When the question is  how to find LCM of 2 3 and 5, you need to tell the smallest positive number that is a multiple of all three. This idea is very important for Class 7 pupils to understand because it provides the basis for adding fractions with different denominators and solving difficult timing issues. Knowing how to compute the LCM of 2, 3, and 5 using different approaches will always give you a way to double-check your work, whether you're doing mental maths or getting ready for school tests. This guide explains the best ways to help you understand this important maths idea.

What is LCM of 2, 3, and 5?

The abbreviation LCM means "Least Common Multiple". For the integers 2, 3, and 5, we want to find the "first" number that shows up in all three of their multiplication tables.

The only number that 2, 3, and 5 have in common is 1 because they are prime numbers.
In mathematics, such numbers are often handled differently than composite numbers. The LCM of 2 3 and 5 is the smallest value that can be divided by 2, 3, and 5 without leaving any remainder.

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Why the LCM of 2, 3 & 5 is 30?

If you look at the multiples:

• Multiples of 2: 2, 4, 6, ..., 28, 30, 32

• Multiples of 3: 3, 6, 9, ..., 27, 30, 33

• Multiples of 5: 5, 10, 15, 20, 25, 30, 35

As you can see, 30 is the very first number that shows up in every single list.

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Different Methods to Find LCM of 2 3 and 5

There isn't just one way to solve this problem. Depending on your preference or the requirements of your assignment, you can choose from three main strategies to find the LCM of 2, 3 & 5:

1. The Listing Multiples Method

This is often considered the most straightforward lcm method for class 4 and 5 learners. It involves writing out the tables for each number until you spot a match.

• Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

• Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

• Multiples of 5: 5, 10, 15, 20, 25, 30

The smallest number that is common to all three lists is 30. Therefore, the lcm of 2 3 and 5 is 30.

2. The Prime Factorisation Method

This method is highly efficient for larger numbers, but it works perfectly here too. You break each number down into its prime factors.

• 2 is a prime factor of 2.

• The prime factor of 3 is 3.

• The number 5 is a prime factor of 5.

You just multiply the maximum power of each prime factor in the three numbers because they are all prime:

The least common multiple (LCM) is 30.

3. The Common Division Method

Also known as the ladder method, this involves dividing the numbers together by prime factors until you reach 1.

1. Place 2, 3, and 5 in a row.

2. Divide by the smallest prime (2): You get 1, 3, 5.

3. Divide by the next prime (3): You get 1, 1, 5.

4. Divide by the next prime (5): You get 1, 1, 1.

5. Multiply the divisors: 2 × 3 × 5 = 30.

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LCM of 2 3 and 5 Examples in Daily Life

It becomes a lot easier to understand what the LCM of 2, 3, and 5 is when you use it in real life. This math is useful in several situations:

• Traffic Lights: Picture three different traffic lights. Every two minutes, one turns green; every three minutes, another turns green; and every five minutes, a third turns green. If they all turn green at noon, they will turn green again at the same time, 30 minutes later, at 12:30 PM.

• Medicine Doses: If a patient needs to take three separate tablets every two, three, and five hours, they will take all three pills at the same time every thirty hours.

• School Bells: In a large school, if three different bells ring at intervals of 2, 3, and 5 minutes, they will chime together every 30 minutes.
  When calculating the LCM of 2, 3 and 5, keep these rules in mind:

• The product of any group of prime numbers is always their LCM.

• The LCM will never be smaller than the largest number in your set (in this case, 5).

• The least common multiple of 2, 3, and 5 is 30, and every multiple of 30 is likewise a common multiple of 2, 3, and 5.

Comparison Table for Quick Reference of LCM

LCM of 2, 3 & 5 Summary

To find the LCM of 2 3 and 5, you can use the listing method, prime factorisation, or division. Because these numbers are coprime (they share no factors other than 1), the quickest way is to multiply them. This concept is a staple in the Curious Jr Mental Math curriculum, helping students develop a faster "feel" for numbers.

By practising how to find the LCM of 2 3 and 5, you build the mental stamina required for more advanced algebra and arithmetic later in your academic journey.

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