LCM of 4 and 6

LCM of 4 and 6 is 12. Least Common Multiple is often called LCM. LCM is the method to find the common positive integer divisible by the given set of numbers. LCM can be calculated by using the division method and prime factorization method.

In this article, we will learn what is LCM of 4 and 6 and how to find it using different methods.

What is LCM of 4 and 6?

Least Common Multiple (LCM) of 4 and 6 is the smallest positive integer that can be divided by both 4 and 6 without leaving a remainder. LCM or Lowest Common Multiple of 4 and 6 is 12.

LCM of 4 and 6 Calculator

How to Find LCM of 4 and 6

To find the Least Common Multiple (LCM) of 4 and 6, you can employ any of the below methods and follow the steps to get the desired LCM of 4 and 6.

• LCM of 4 and 6 by Prime Factorization
• LCM of 4 and 6 by Listing Multiples
• LCM of 4 and 6 by Long Division

LCM of 4 and 6 by Prime Factorization

Follow the below mentioned steps to find the LCM of 4 and 6 using Prime Factorization

Step 1: Find the Prime Factorization of 4 and 6

• Prime factorization of 4 is 2²
• Prime factorization of 6 is 2 × 3

Step 2: Identify the Highest Powers of

• The highest power of 2 is 2²
• The highest power of 3 is 3¹

Step 3: Multiply the Highest Powers

• LCM (4,6)= 2² × 3¹ = 12

Hence, Least Common Multiple (LCM) of 4 and 6 by prime factorization is 12.

LCM of 4 and 6 by Listing Multiples

Use the following steps to find the multiples of 4 and 6 by listing multiple method

Step 1: List the Multiples of 4 and 6

• The multiples of 4 are 4, 8, 12, 16, 20, 24… and so on
• The multiples of 6 are 6, 12, 18, 24, 30… and so on

Step 2: Identify the Smallest Common Multiple

• The smallest common multiple comes out to be 12.

Hence, Least Common Multiple of 4 and 6 is 12.

LCM of 4 and 6 by Long Division

Use the following steps to find the multiples of 4 and 6 by listing multiple method

Step 1: Begin by dividing the given numbers with the smallest prime integer.

Step 2: In the subsequent row, record both the quotient and any number that is not divisible by the prime number in step 1.

Step 3: Proceed to divide the integers by the next lowest prime number in the sequence.

Step 4: Continue this division process until the remaining number is a prime number or reaches one.

Step 5: To determine the Least Common Multiple (LCM), multiply all the divisors along with the remaining prime number as shown below

LCM of 6 and 4 is 2 × 2 × 3 = 12

LCM of 6 and 4

LCM of 6 and 4 is 12. It is same as that of LCM of 4 and 6. LCM of given set of number is same irrespective of the order in which they are arranged

Solved Examples on LCM of 6 and 4

Example 1: A bakery churning out batches of 4 cookies and 6 muffins. To share equally, what is the minimum number of batches needed?

Solution:

To find the minimum number of cookies and muffins that need to be shared equally we need to find LCM of 4 and 6.

LCM of 4 and 6 is 12

Hence, 12 batches are needed to equally share 4 cookies and 6 muffins

Example 2: Two friends have watering schedules for their plants one every 4 days, the other every 6. When will their watering days align again?

Solution:

To find the same watering day we have to find the day which is divisible by 4 and 6

LCM of 4 and 6 is 12.

Hence, they will again water the plants together on 12th day.

Example 3: There are 4 red and 6 blue marbles. If you want to split them equally into bags, what’s the minimum number of marbles you need

Solution:

To equally distribute them into bags We have to find the LCM of 4 and 6 (12).

Hence, we need total of 12 marbles to equally distribute in bags

Practice Problems on LCM of 4 and 6

Q1: Calculate the LCM of 4 and 6 using prime factorization?

Q2: List the multiples of 4 and 6 and identify their least common multiple?

Q3: Using long division, find the LCM of 4 and 6?

Q4: If two events occur at intervals of 4 and 6 hours, when will they next occur simultaneously?

Q5: A factory has two machines that need maintenance every 4 and 6 hours, respectively. When will both machines need maintenance on the same day?

Q6: A gardener waters plants every 4 days and fertilizes them every 6 days. How often will the gardener water and fertilize the plants on the same day?

Q7: Find the LCM of 4 and 6 and use it to simplify the fraction 3/4 × 5/6?

Q8: A bus departs from a station every 4 hours, and another departs every 6 hours. After how many hours will both buses depart simultaneously?

LCM of 4 and 6 FAQs

What does LCM stand for?

LCM stands for “Least Common Multiple.”

How is the LCM of 4 and 6 calculated by prime factorization?

To find the LCM of 4 and 6 by prime factorization, identify the prime factors of each number and multiply the highest powers. For 4 and 6, the LCM is 2²×3¹=12.

Can the LCM be found by listing multiples?

Yes, listing multiples is another method. Identify the common multiple by listing multiples of each number and finding the smallest one. For 4 and 6, the LCM is 12.

Can the LCM be larger than the given Numbers?

Yes, the LCM can be larger than the given numbers

What is LCM of 4, 5 and 6?

LCM of 4, 5 and 6 is 60

What is LCM of 4, 6 and 8?

LCM of 4, 6 and 8 is 24

What is LCM of 4, 6 and 3?

LCM of 4, 6 and 3 is 12