present Steps for functioning Out by: none Listing Multiples prime Factorization Cake / Ladder department Method GCF an approach
*

*

Calculator Use

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

The LCM of two or more numbers is the smallest number the is evenly divisible by every numbers in the set.

You are watching: Common multiples of 6 and 10

Least common Multiple Calculator

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

Input the number you desire to find the LCM for. You deserve to use commas or spaces to separate your numbers. But do not use commas within your numbers. For example, enter 2500, 1000 and also not 2,500, 1,000.

See more: How Many Quarters Do You Need To Make A Dollar S? (Answer + Fast Calculator)

How to uncover the Least typical Multiple LCM

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

Listing Multiples prime Factorization Cake/Ladder Method division Method using the Greatest common Factor GCF

How to uncover LCM through Listing Multiples

perform the multiples of each number until at the very least one that the multiples shows up on every lists discover the smallest number the is on all 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 that 21: 21, 42, 63 find the smallest number the is on every one 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 components of each provided number. Perform all the prime numbers found, as many times together they happen most regularly for any kind of one offered number. Multiply the perform of prime factors together to find the LCM.

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

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

prime factorization of 12 = 2 × 2 × 3 element factorization that 30 = 2 × 3 × 5 making use of all prime numbers found as frequently as each occurs most often we take it 2 × 2 × 3 × 5 = 60 as such LCM(12,30) = 60.

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

prime factorization that 24 = 2 × 2 × 2 × 3 element factorization the 300 = 2 × 2 × 3 × 5 × 5 using all element numbers discovered as regularly as each occurs most frequently we take 2 × 2 × 2 × 3 × 5 × 5 = 600 thus LCM(24,300) = 600.

How to uncover LCM by element Factorization utilizing Exponents

discover all the prime factors of each provided number and write them in exponent form. List all the element numbers found, making use of the highest possible exponent uncovered for each. Main point the perform of prime components with exponents together to uncover the LCM.

Example: LCM(12,18,30)

Prime factors of 12 = 2 × 2 × 3 = 22 × 31 Prime factors of 18 = 2 × 3 × 3 = 21 × 32 Prime determinants of 30 = 2 × 3 × 5 = 21 × 31 × 51 perform all the prime numbers found, as plenty of times together they occur most regularly for any kind of one given number and multiply them with each other to uncover the LCM 2 × 2 × 3 × 3 × 5 = 180 using exponents instead, multiply together each that the prime numbers through the highest power 22 × 32 × 51 = 180 so 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 perform all the prime numbers found, as plenty of times together they take place most frequently for any kind of one provided number and multiply them together to find the LCM 2 × 2 × 2 × 3 × 5 × 5 = 600 making use of exponents instead, multiply with each other each of the prime numbers through the highest possible power 23 × 31 × 52 = 600 therefore LCM(24,300) = 600

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

The cake technique uses department to uncover the LCM the a collection of numbers. Human being use the cake or ladder technique as the fastest and also easiest way to find the LCM due to the fact that it is an easy division.

The cake technique is the exact same as the ladder method, package method, the aspect box technique and the grid an approach of shortcuts to uncover the LCM. The boxes and grids might look a small different, however they all use department by primes to discover LCM.