Show measures for working Out by: nobody Listing Multiples prime Factorization Cake / Ladder department Method GCF method
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The Least common Multiple (LCM) is also referred to as the Lowest usual Multiple (LCM) and also Least typical Divisor (LCD). For two integers a and b, denoted LCM(a,b), the LCM is the smallest optimistic integer that is same divisible by both a and b. For example, LCM(2,3) = 6 and LCM(6,10) = 30.

The LCM of 2 or much more numbers is the the smallest number that is same divisible by every numbers in the set.

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Least common Multiple Calculator

Find the LCM of a set of numbers v this calculator which likewise shows the steps and how to perform the work.

Input the number you want to find the LCM for. You can use commas or spaces to different your numbers. However do not use commas within her numbers. Because that example, get in 2500, 1000 and not 2,500, 1,000.

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How to find the Least common Multiple LCM

This LCM calculator with actions finds the LCM and shows the job-related using 5 different methods:

Listing Multiples element Factorization Cake/Ladder Method department Method making use of the Greatest typical Factor GCF

How to discover LCM by Listing Multiples

list the multiples of each number until at least one that the multiples shows up on every lists uncover the smallest number that is on all of the perform This number is the LCM

Example: LCM(6,7,21)

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 Multiples of 7: 7, 14, 21, 28, 35, 42, 56, 63 Multiples the 21: 21, 42, 63 find the the smallest number that is on every one of the lists. We have it in bolder above. Therefore LCM(6, 7, 21) is 42

How to uncover LCM by prime Factorization

uncover all the prime determinants of each offered number. Perform all the prime numbers found, as plenty of times as they occur most frequently for any kind of one given number. Multiply the list of prime components together to find the LCM.

The LCM(a,b) is calculated by recognize the element factorization of both a and b. Usage the same procedure for the LCM of much more than 2 numbers.

For example, for LCM(12,30) we find:

element factorization the 12 = 2 × 2 × 3 prime factorization that 30 = 2 × 3 × 5 using all prime numbers uncovered as frequently as every occurs most regularly we take 2 × 2 × 3 × 5 = 60 because of this LCM(12,30) = 60.

For example, for LCM(24,300) us find:

prime factorization the 24 = 2 × 2 × 2 × 3 prime factorization that 300 = 2 × 2 × 3 × 5 × 5 utilizing all prime numbers found as often as every occurs most frequently we take 2 × 2 × 2 × 3 × 5 × 5 = 600 therefore LCM(24,300) = 600.

How to find LCM by prime Factorization using Exponents

find all the prime components of each provided number and write lock in exponent form. List all the element numbers found, making use of the highest exponent found for each. Multiply the list of prime factors with exponents together to discover the LCM.

Example: LCM(12,18,30)

Prime components of 12 = 2 × 2 × 3 = 22 × 31 Prime determinants of 18 = 2 × 3 × 3 = 21 × 32 Prime components of 30 = 2 × 3 × 5 = 21 × 31 × 51 list all the prime numbers found, as plenty of times as they occur most frequently for any type of one provided number and multiply them with each other to uncover the LCM 2 × 2 × 3 × 3 × 5 = 180 utilizing exponents instead, multiply together each that the prime numbers with the highest power 22 × 32 × 51 = 180 therefore LCM(12,18,30) = 180

Example: LCM(24,300)

Prime determinants of 24 = 2 × 2 × 2 × 3 = 23 × 31 Prime components of 300 = 2 × 2 × 3 × 5 × 5 = 22 × 31 × 52 list all the element numbers found, as numerous times together they occur most frequently for any one provided number and also multiply them together to uncover the LCM 2 × 2 × 2 × 3 × 5 × 5 = 600 making use of exponents instead, multiply together each of the prime numbers through the greatest power 23 × 31 × 52 = 600 for this reason LCM(24,300) = 600

How to find LCM utilizing the Cake method (Ladder Method)

The cake an approach uses department to uncover the LCM of a collection of numbers. Civilization use the cake or ladder technique as the fastest and easiest means to discover the LCM due to the fact that it is basic division.

The cake technique is the same as the ladder method, the box method, the aspect box technique and the grid an approach of shortcuts to uncover the LCM. The boxes and also grids could look a small different, but they every use department by primes to find LCM.