LCM of 12 and 18

LCM also called Least Common Multiple of two numbers is the smallest multiple that both numbers can divide evenly without leaving any remainder. In this article, we will learn what is LCM of 12 and 18, How to Find LCM of 12 and 18 using different methods and solve examples based on it.

What is LCM of 12 and 18?

Answer: LCM of 12 and 18 is 36

LCM of 12 and 18 is the smallest number that is divisible by both 12 and 18. It is the smallest multiple that these numbers share in common. The LCM of 12 and 18 is 36. This means 36 is the smallest common multiple of 12 and 18 which is divisible by both the number 12 and 18.

LCM of 12 and 18 Calculator

Try out the following calculator to find LCM of 12 and 18:

How to Find LCM of 12 and 18

We can find LCM of 12 and 18 using the following three methods

• By Prime Factorization
• By Listing Multiples
• By Division

LCM of 12 and 18 by Prime Factorization

To find the LCM of 12 and 18 by Prime Factorization use the following steps:

• Step 1: Express each number as a product of prime numbers.
• Step 2: Take each prime factor as many times as the highest number of times it appears.
• Step 3: The product of the prime factors selected in step 2 is the LCM of the number

On Prime factorization

• 12 = 2 × 2 × 3
• 18 = 2 × 3 × 3

Here, 2 appears twice and 3 also appears twice .

So LCM = 2 × 2 × 3 × 3 = 36

LCM of 12 and 18 by Listing Method

The multiples of 12 = 12, 24, 36, 48, 60, . . .

The multiples of 18 = 18, 36, 54, 72, . . .

The common multiples of 12 and 18 are 36, 72 , . . .

Among these 36 is the lowest common multiple

LCM of 12 and 18 = 36

LCM of 12 and 18 by Division

To find the LCM of 12 and 18 by Division Method try the following steps:

• Step 1: Divide the numbers 12 and 18 by a number which is a factor of at least two of the numbers.
• Step 2: Write the quotients and carry forward the numbers which are not divisible.
• Step 3: Repeat the steps 1 and 2 till no two of the numbers has a common factor.
• Step 4: Find the product of the divisors of all the steps and the remaining numbers is the LCM of the numbers.

LCM of 12 and 18

LCM of 12 and 18 = 2 × 2 × 3 × 3 = 36

LCM vs HCF of 12 and 18

LCM is the smallest multiple that both numbers can divide into evenly. For the case of 12 and 18, the LCM would be the smallest number that both 6 and 9 can evenly divide into without the remainder.

HCF is the biggest number that can divide both 12 and 18, leaving no remainder. HCF of 12 and 18 is 3.

LCM focuses on finding the smallest shared multiple, while HCF looks for the largest shared divisor.

Examples on LCM of 12 and 18

Example 1: Two measuring rods are 12 cm and 18 cm in length. What is the least length of a rope that can be measured by the full length of each of these rods?

Solution:

The least length of rope that can be measured by the full length of each of these rods is the least common multiple (LCM) of their lengths.

The LCM of 12 and 18 is 36.

So, the least length of rope that can be measured is 36 cm.

Example 2: Two bells toll at intervals of 12 mins and 18 mins. If they start tolling together, after what time will they next toll together?

Solution:

To find when the bells will next toll together, we need to find the least common multiple (LCM) of their tolling intervals, which are 12 minutes and 18 minutes.

The LCM of 12 and 18 is 36. So, the bells will next toll together after 36 minutes.

LCM of 12 and 18 Practice Questions

Q1: Find the difference between twice the LCM and the HCF of 12 and 18.

Q2: Find the square of the HCF of 12 and 18 subtracted from the LCM.

Q3: If the LCM of 12 and 18 is divided by their HCF, what is the quotient?

Q4: Which of the following is the LCM of 12 and 18?

• 50
• 15
• 45
• 36

LCM of 12 and 18 Frequently Asked Questions

What does LCM stand for?

LCM stands for Least Common Multiple.

What is the LCM of 12 and 18?

The LCM of 12 and 18 is 36.

How do you find the LCM of 12 and 18?

We can find the LCM of 12 and 18 using various methods such as Prime Factorization method, listing multiples method and division method.

Why is 36 the least common multiple of 12 and 18?

36 is the least common multiple of 12 and 18 because it is the smallest positive integer that is divisible by both 12 and 18 without leaving a remainder.

Can the LCM of two numbers ever be smaller than either of the numbers?

No, the LCM of two numbers is always equal to or greater than the larger of the two numbers. This is because the LCM represents the smallest common multiple of the numbers, so it must be at least as large as the largest individual number.