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Last updated on November 30th, 2024

LCM of 12 and 18

Q: Why is the LCM of 12 and 18 not simply their product (12 × 18 = 216)?

Multiplying gives you the product of the numbers, in this case,216. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method.

Q: How do you find the LCM of 12 and 18 using a Venn diagram?

Follow the below steps to ascertain the LCM of 10 and 12 using a Venn diagram; List the prime factors of the digits — Prime factorization of 12 = 2 × 2 × 3 → 2×3 — Prime factorization of 18 = 2 × 3 × 3 → 2×32 Place the factors in the diagram 2 and 3 are common factors, place it in the overlapping section. 2,3 are unique factors ascertained after the common factor for 12 and 18. Place them in their own section. Now, multiply both the common and the unique factors — 2 × 2 × 3×3 = 36 The LCM (12,18) = 36.

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 12 and 18, HCF(12,18)= 6 So, LCM(12,18)=12×18/6 = 36

Q: If both the numbers are prime, what is the LCM? Explain in the case of 12 and 18.

If both the numbers are prime, their LCM will be the product of the numbers as they do not share any common factors but 1. However, 12 and 18 are non-prime numbers/composite numbers, i.e, they share a common factor, therefore their LCM is 36.

Q: How can you check if the LCM you ascertained is right? Explain using the digits 12 and 18.

The LCM ascertained can be verified in the following way; — LCM of the numbers 12 and 18 is 36. — Divide the LCM with the digits, i.e., 36/12 = 3, 36/18 =2. — The results are whole numbers, i.e., there are no reminders left behind, therefore we can conclude the LCM ascertained is right.

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 12 and 18. 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 12 and 18?

The LCM of 12 and 18 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 12 and 18?

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;

LCM of 12 and 18 using the Listing Multiples Method

The LCM of 12 and 18 can be found using the following steps:

Steps:

List the multiples of each number

— Multiples of 12 = 12, 24, 36, 48, 60, 72, …

— Multiples of 18 = 18, 36, 54, 72, 90, …

Figure the smallest multiple from the listed multiples

— The smallest common multiple is 36.

Thus, LCM(12, 18) = 36

LCM of 12 and 18 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:

Devise prime factors of the given numbers:

— Prime factorization of 12 = 2 × 2 × 3

— Prime factorization of 18 = 2 × 3 × 3

Pick the highest powers of each prime factor:

— Highest power of 2 = 2²

— Highest power of 3 = 3²

Find the product of the highest powers to get the LCM:

LCM(12, 18) = 2² × 3² = 36.

LCM of 12 and 18 using the Division Method

This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to get the LCM.

Steps:

Write the numbers:

Divide by common prime factors and multiply the divisors:

— 2 × 2 × 3 × 3 = 36

Thus, LCM(12, 18) = 36.

Common Mistakes and how to avoid them while finding the LCM of 12 and 18

LCM of 12 and 18 examples

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

Goods are received by a shipping company every 12 and 18 days. If the shipments have been received today, when will they next arrive at, the same day?

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

Explanation

Problem 2

A maintenance schedule for projectors is set up every 12 weeks and 18 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 3

Two clocks strike every 12 hours and 18 hours. If both of them strike now, when will they next strike together?

Explanation

Problem 4

In a neighborhood park, the fountain show is turned on every 12 minutes, and the light show every 18 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?

Explanation

Problem 5

A car mechanic services a red car every 12 days and a blue car every 18 days. If the cars are serviced today, when will they be serviced next together?

Explanation

FAQs on LCM of 12 and 18

1.Why is the LCM of 12 and 18 not simply their product (12 × 18 = 216)?

2.How do you find the LCM of 12 and 18 using a Venn diagram?

3.What is the LCM formula using the HCF?

4.If both the numbers are prime, what is the LCM? Explain in the case of 12 and 18.

5.How can you check if the LCM you ascertained is right? Explain using the digits 12 and 18.

Important glossaries for the LCM of 12 and 18

Multiple: A number and any integer multiplied.
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.