LCM the 12 and 36 is the the smallest number amongst all typical multiples the 12 and 36. The first few multiples of 12 and also 36 space (12, 24, 36, 48, 60, 72, 84, . . . ) and (36, 72, 108, 144, 180, 216, 252, . . . ) respectively. There space 3 commonly used methods to find LCM the 12 and 36 - by listing multiples, by prime factorization, and also by division method.

You are watching: Find the least common factor of 12 and 36

1.LCM that 12 and also 36
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM of 12 and also 36 is 36.

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Explanation:

The LCM of 2 non-zero integers, x(12) and also y(36), is the smallest positive integer m(36) the is divisible by both x(12) and also y(36) without any type of remainder.


The approaches to discover the LCM the 12 and 36 are described below.

By prime Factorization MethodBy division MethodBy Listing Multiples

LCM that 12 and 36 by prime Factorization

Prime administrate of 12 and also 36 is (2 × 2 × 3) = 22 × 31 and also (2 × 2 × 3 × 3) = 22 × 32 respectively. LCM of 12 and 36 have the right to be derived by multiply prime determinants raised to their respective highest power, i.e. 22 × 32 = 36.Hence, the LCM the 12 and also 36 by element factorization is 36.

LCM that 12 and 36 by department Method

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To calculation the LCM of 12 and also 36 by the department method, we will certainly divide the numbers(12, 36) by your prime determinants (preferably common). The product of this divisors offers the LCM that 12 and 36.

Step 3: continue the actions until just 1s space left in the critical row.

The LCM the 12 and also 36 is the product of every prime numbers on the left, i.e. LCM(12, 36) by division method = 2 × 2 × 3 × 3 = 36.

LCM of 12 and 36 by Listing Multiples

To calculation the LCM that 12 and also 36 through listing out the common multiples, we can follow the given listed below steps:

Step 1: perform a couple of multiples the 12 (12, 24, 36, 48, 60, 72, 84, . . . ) and also 36 (36, 72, 108, 144, 180, 216, 252, . . . . )Step 2: The typical multiples native the multiples the 12 and 36 are 36, 72, . . .Step 3: The smallest typical multiple of 12 and 36 is 36.

∴ The least typical multiple of 12 and also 36 = 36.

☛ likewise Check:


Example 1: Verify the relationship in between GCF and also LCM of 12 and 36.

Solution:

The relation in between GCF and LCM that 12 and also 36 is given as,LCM(12, 36) × GCF(12, 36) = Product the 12, 36Prime factorization of 12 and 36 is given as, 12 = (2 × 2 × 3) = 22 × 31 and also 36 = (2 × 2 × 3 × 3) = 22 × 32LCM(12, 36) = 36GCF(12, 36) = 12LHS = LCM(12, 36) × GCF(12, 36) = 36 × 12 = 432RHS = Product of 12, 36 = 12 × 36 = 432⇒ LHS = RHS = 432Hence, verified.


Example 3: find the the smallest number that is divisible by 12 and 36 exactly.

Solution:

The the smallest number the is divisible by 12 and 36 precisely is your LCM.⇒ Multiples of 12 and also 36:

Multiples the 12 = 12, 24, 36, 48, 60, 72, . . . .Multiples of 36 = 36, 72, 108, 144, 180, 216, . . . .

Therefore, the LCM the 12 and also 36 is 36.


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FAQs top top LCM that 12 and 36

What is the LCM the 12 and also 36?

The LCM the 12 and 36 is 36. To discover the LCM (least usual multiple) the 12 and also 36, we need to discover the multiples of 12 and 36 (multiples of 12 = 12, 24, 36, 48; multiples that 36 = 36, 72, 108, 144) and also choose the the smallest multiple that is precisely divisible through 12 and also 36, i.e., 36.

What space the approaches to discover LCM of 12 and also 36?

The commonly used approaches to discover the LCM that 12 and 36 are:

Division MethodPrime factorization MethodListing Multiples

Which the the following is the LCM that 12 and also 36? 2, 25, 5, 36

The worth of LCM that 12, 36 is the smallest typical multiple that 12 and also 36. The number to solve the given problem is 36.

If the LCM the 36 and also 12 is 36, uncover its GCF.

LCM(36, 12) × GCF(36, 12) = 36 × 12Since the LCM of 36 and 12 = 36⇒ 36 × GCF(36, 12) = 432Therefore, the GCF (greatest usual factor) = 432/36 = 12.

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What is the Relation between GCF and LCM the 12, 36?

The following equation deserve to be provided to refer the relation in between GCF and also LCM the 12 and also 36, i.e. GCF × LCM = 12 × 36.