present Steps for working Out by: nobody Listing Multiples element Factorization Cake / Ladder division Method GCF an approach
*

*

Calculator Use

The Least common Multiple (LCM) is likewise referred to as the Lowest usual Multiple (LCM) and also Least common Divisor (LCD). For two integers a and b, denoted LCM(a,b), the LCM is the smallest hopeful integer that is evenly divisible through both a and also b. Because that example, LCM(2,3) = 6 and LCM(6,10) = 30.

The LCM of 2 or much more numbers is the the smallest number the is evenly divisible by all numbers in the set.

You are watching: What is the lcm of 3 9 and 12

Least common Multiple Calculator

Find the LCM of a set of numbers with this calculator which additionally shows the steps and also how to carry out the work.

Input the number you want to uncover the LCM for. You can use commas or spaces to separate your numbers. However do not usage commas within her numbers. Because that example, go into 2500, 1000 and also not 2,500, 1,000.

See more: Narrator And Point Of View Of Miss Brill By Katherine Mansfield

How to find the Least usual Multiple LCM

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

Listing Multiples prime Factorization Cake/Ladder Method department Method utilizing the Greatest typical Factor GCF

How to uncover LCM through Listing Multiples

perform the multiples of every number till at the very least one the the multiples appears on every lists uncover the smallest number that is on every one of the list This number is the LCM

Example: LCM(6,7,21)

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

How to find LCM by element Factorization

discover all the prime determinants of each provided number. List all the prime numbers found, as plenty of times together they take place most frequently for any one offered number. Main point the perform of prime determinants together to uncover the LCM.

The LCM(a,b) is calculate by detect the prime factorization the both a and also b. Use the same process for the LCM of an ext than 2 numbers.

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

prime factorization the 12 = 2 × 2 × 3 prime factorization the 30 = 2 × 3 × 5 utilizing all element numbers discovered as often as every occurs most often we take it 2 × 2 × 3 × 5 = 60 because of this LCM(12,30) = 60.

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

element factorization that 24 = 2 × 2 × 2 × 3 element factorization of 300 = 2 × 2 × 3 × 5 × 5 utilizing all prime numbers found as frequently as each occurs most frequently we take it 2 × 2 × 2 × 3 × 5 × 5 = 600 thus LCM(24,300) = 600.

How to uncover LCM by prime Factorization utilizing Exponents

uncover all the prime components of each given number and write castle in exponent form. List all the prime numbers found, utilizing the greatest exponent uncovered for each. Multiply the perform of prime determinants with exponents with each other to find the LCM.

Example: LCM(12,18,30)

Prime components of 12 = 2 × 2 × 3 = 22 × 31 Prime factors of 18 = 2 × 3 × 3 = 21 × 32 Prime factors of 30 = 2 × 3 × 5 = 21 × 31 × 51 perform all the element numbers found, as many times as they occur most regularly for any one given number and multiply them with each other to uncover the LCM 2 × 2 × 3 × 3 × 5 = 180 utilizing exponents instead, multiply together each of the element numbers v the highest power 22 × 32 × 51 = 180 therefore LCM(12,18,30) = 180

Example: LCM(24,300)

Prime components of 24 = 2 × 2 × 2 × 3 = 23 × 31 Prime components of 300 = 2 × 2 × 3 × 5 × 5 = 22 × 31 × 52 perform all the prime numbers found, as plenty of times together they take place most often for any type of one given number and also multiply them with each other to discover the LCM 2 × 2 × 2 × 3 × 5 × 5 = 600 utilizing exponents instead, multiply with each other each of the prime numbers with the highest power 23 × 31 × 52 = 600 so LCM(24,300) = 600

How to discover LCM utilizing the Cake technique (Ladder Method)

The cake method uses division to uncover the LCM the a set of numbers. People use the cake or ladder method as the fastest and easiest means to find the LCM due to the fact that it is straightforward division.

The cake technique is the same as the ladder method, package method, the variable box technique and the grid an approach of shortcuts to discover the LCM. The boxes and grids might look a little different, but they every use division by primes to discover LCM.