display Steps for functioning Out by: none Listing Multiples element Factorization Cake / Ladder department Method GCF technique  ## Calculator Use

The Least typical Multiple (LCM) is likewise referred to together the Lowest usual Multiple (LCM) and Least typical Divisor (LCD). For 2 integers a and b, denoted LCM(a,b), the LCM is the smallest positive integer the is same divisible by both a and b. Because that example, LCM(2,3) = 6 and LCM(6,10) = 30.

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

You are watching: What is the least common multiple of 3 and 12

## Least usual Multiple Calculator

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

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

See more: How Much Does Brooke Shields Weigh T Body Vital Stats Facts Bio

## How to uncover the Least typical Multiple LCM

This LCM calculator with procedures finds the LCM and also shows the occupational using 5 different methods:

Listing Multiples element Factorization Cake/Ladder Method division Method making use of the Greatest common Factor GCF

## How to find LCM by Listing Multiples

perform the multiples of each number till at the very least one of the multiples appears on every lists uncover the smallest number the 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 the 7: 7, 14, 21, 28, 35, 42, 56, 63 Multiples the 21: 21, 42, 63 find the the smallest number that is on all of the lists. We have actually it in bolder above. So LCM(6, 7, 21) is 42

## How to discover LCM by prime Factorization

discover all the prime factors of each given number. List all the element numbers found, as numerous times as they happen most frequently for any kind of one given number. Main point the perform of prime factors together to find the LCM.

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

For example, because that LCM(12,30) us find:

element factorization the 12 = 2 × 2 × 3 element 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 therefore LCM(12,30) = 60.

For example, because that LCM(24,300) us find:

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

## How to uncover LCM by prime Factorization making use of Exponents

uncover all the prime components of each provided number and also write castle in exponent form. Perform all the element numbers found, using the greatest exponent uncovered for each. Main point the perform of prime determinants with exponents with each other to uncover the LCM.

Example: LCM(12,18,30)

Prime factors 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 together they take place most frequently for any type of one offered number and multiply them together to uncover the LCM 2 × 2 × 3 × 3 × 5 = 180 using exponents instead, multiply with each other each the the prime numbers with the greatest power 22 × 32 × 51 = 180 for this reason 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 element numbers found, as many times as they happen most regularly for any type of 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 element numbers through the greatest power 23 × 31 × 52 = 600 so LCM(24,300) = 600

## How to discover LCM utilizing the Cake an approach (Ladder Method)

The cake technique uses department to find the LCM the a set of numbers. Human being use the cake or ladder an approach as the fastest and also easiest way to discover the LCM since it is straightforward division.

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