421 LearnersLast updated on May 26th, 2025
LCM of 4 and 6
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 4 and 6. 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 4 and 6?
The LCM of 4 and 6 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 4 and 6 ?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 4 and 6 using the Listing Multiples method
The LCM of 4 and 6 can be found using the following steps;
Steps:
1. Write down the multiples of each number:
- Multiples of 4 = 4,8,12,16…
- Multiples of 6 = 6,12,18,24…
2. Ascertain the smallest multiple from the listed multiples of 4 and 6.
The LCM (Least common multiple) 4 and 6 is 12, i.e.,12 is divisible by 4 and 6 leaving no reminders.
LCM of 4 and 6 using the Prime Factorization
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Steps:
1. Find the prime factors of the numbers:
Prime factorization of 4 = 2×2
Prime factorization of 6 = 2×3
2. Take the highest power of each prime factor:
— 2,2,3
3. Multiply the ascertained factors to get the LCM:
LCM (4,12) = 2×2×3 = 12
LCM of 4 and 6 using the Division Method
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Steps:
1. Write down the numbers in a row;
2. Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers.
3. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers has not been divisible previously.
4. The LCM of the numbers is the product of the prime numbers in the first column, i.e,
2×2×3= 12
LCM (4,6) = 12
Common Mistakes and how to avoid them while finding the LCM of 4 and 6
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 4 and 6, make a note while practicing.
Mistake 1
Listing incorrect/overlooking multiples for the given numbers 4 and 6
This can be avoided by always double-checking the multiples of the numbers 4 and 6 and by not stopping too early. To elaborate, listing 4,8, as multiples of 4 and 6,12 as the multiples of 6 and assuming 4 is the LCM.
Mistake 2
Confusing between LCM and HCF of the numbers 4 and 6.
This can be avoided by learning that the LCM deals with multiples of the numbers 4 and 6, while HCF focuses on divisors of, 4 and 6i.e., the HCF of 4 and 6 is 2, and the LCM is 12.
Mistake 3
Skipping the prime factors of the given numbers.
Errors in prime factorization often include incorrectly factoring 4 and 6. To illustrate, factoring 6 as 23 instead of 2×3. Doing so will yield the wrong LCM.
Mistake 4
Multiplying the numbers directly
Incorrectly assuming that multiplying the numbers 4 and 6 and assuming the product is the LCM instead of finding the lowest multiple.
Mistake 5
Skipping the LCM in the list method
Oven, the first common multiples in the list of multiples are ignored due to an oversight, like 12 that appears on the list of both 4 and 6.
LCM of 4 and 6, Examples
Problem 1
A vendor sells blueberries in boxes of 4 and cranberries boxes of 6. What is the smallest number of boxes that must be purchased, to have an equal number of the berries ?
The LCM of 4 and 6 is 12.
Explanation
12 boxes of blueberries and cranberries are to be purchased to have an equal number of each, as the smallest common multiple between the numbers 4 and 6 is 12.
Problem 2
At a school, two bells ring at 4-minute and 6-minute intervals. If they ring together at 10 AM, when will they ring together again?
The LCM of 4 and 6 is 12.
Explanation
They will ring together again after 12 minutes, which is at 10:12 AM. The smallest common multiple of 4 and 6 is 12.
Problem 3
Runner A can complete a lap in 4 minutes, and Runner B can complete a lap in 6 minutes. When will runners A and B meet at again?
LCM of 4 and 6.
Explanation
Runners A and B will meet again after 12 minutes, which is the LCM of 4 and 6.
Problem 4
Alex and Ben want to share a pizza, but they can’t decide how many slices to cut into. Alex says 4, and Ben says 6. What is the minimum number of slices they can cut the pizza into so that both can have their desired number of slices without leftovers?
The LCM of 4 and 6 is 12.
Explanation
Alex and Ben should cut the pizza into 12 slices, which is the LCM of 4 and 6.
FAQs on LCM of 4 and 6
1.Why is the LCM of 4 and 6 not simply their product (4 × 6 = 24)?
2.What is the relationship between the Highest common Factor (HCF) and LCM of 4 and 6?
3.What is the relationship of the LCM and the HCF between the digits 4 and 6? Elaborate using a formula?
Important glossaries for LCM of 4 and 6
- 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.
Fun Fact
: She loves to read number jokes and games.
