LCM of 20 and 40 is the smallest number amongst all usual multiples the 20 and 40. The first few multiples the 20 and 40 room (20, 40, 60, 80, 100, . . . ) and (40, 80, 120, 160, . . . ) respectively. There space 3 commonly used approaches to discover LCM the 20 and 40 - through listing multiples, by department method, and by element factorization.

You are watching: What is the least common multiple of 20 and 40?

1.LCM of 20 and also 40
2.List that Methods
3.Solved Examples
4.FAQs

Answer: LCM of 20 and also 40 is 40.

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Explanation:

The LCM of 2 non-zero integers, x(20) and also y(40), is the smallest positive integer m(40) the is divisible by both x(20) and also y(40) without any kind of remainder.


The methods to uncover the LCM that 20 and also 40 are defined below.

By element Factorization MethodBy Listing MultiplesBy department Method

LCM the 20 and also 40 by element Factorization

Prime administrate of 20 and 40 is (2 × 2 × 5) = 22 × 51 and (2 × 2 × 2 × 5) = 23 × 51 respectively. LCM that 20 and 40 deserve to be acquired by multiply prime components raised to your respective highest power, i.e. 23 × 51 = 40.Hence, the LCM the 20 and also 40 by prime factorization is 40.

LCM the 20 and 40 by Listing Multiples

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To calculate the LCM that 20 and 40 through listing out the typical multiples, we deserve to follow the given below steps:

Step 1: perform a few multiples the 20 (20, 40, 60, 80, 100, . . . ) and also 40 (40, 80, 120, 160, . . . . )Step 2: The usual multiples from the multiples of 20 and 40 room 40, 80, . . .Step 3: The smallest usual multiple the 20 and also 40 is 40.

∴ The least typical multiple that 20 and 40 = 40.

LCM the 20 and 40 by department Method

To calculate the LCM that 20 and 40 by the department method, we will divide the numbers(20, 40) by your prime factors (preferably common). The product of these divisors provides the LCM of 20 and 40.

Step 3: continue the steps until only 1s are left in the last row.

The LCM the 20 and 40 is the product of every prime number on the left, i.e. LCM(20, 40) by division method = 2 × 2 × 2 × 5 = 40.

☛ additionally Check:


Example 1: Verify the relationship in between GCF and LCM the 20 and also 40.

Solution:

The relation in between GCF and also LCM that 20 and also 40 is provided as,LCM(20, 40) × GCF(20, 40) = Product of 20, 40Prime factorization of 20 and 40 is given as, 20 = (2 × 2 × 5) = 22 × 51 and also 40 = (2 × 2 × 2 × 5) = 23 × 51LCM(20, 40) = 40GCF(20, 40) = 20LHS = LCM(20, 40) × GCF(20, 40) = 40 × 20 = 800RHS = Product the 20, 40 = 20 × 40 = 800⇒ LHS = RHS = 800Hence, verified.


Example 3: find the smallest number that is divisible by 20 and 40 exactly.

Solution:

The smallest number the is divisible by 20 and also 40 exactly is their LCM.⇒ Multiples that 20 and also 40:

Multiples of 20 = 20, 40, 60, 80, 100, 120, . . . .Multiples the 40 = 40, 80, 120, 160, 200, 240, . . . .

Therefore, the LCM the 20 and also 40 is 40.


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FAQs on LCM of 20 and also 40

What is the LCM the 20 and also 40?

The LCM of 20 and 40 is 40. To find the LCM (least typical multiple) that 20 and 40, we require to find the multiples of 20 and also 40 (multiples of 20 = 20, 40, 60, 80; multiples that 40 = 40, 80, 120, 160) and choose the the smallest multiple that is specifically divisible through 20 and 40, i.e., 40.

What room the approaches to find LCM of 20 and 40?

The commonly used techniques to uncover the LCM the 20 and 40 are:

Division MethodListing MultiplesPrime administer Method

If the LCM that 40 and also 20 is 40, discover its GCF.

LCM(40, 20) × GCF(40, 20) = 40 × 20Since the LCM of 40 and 20 = 40⇒ 40 × GCF(40, 20) = 800Therefore, the greatest typical factor = 800/40 = 20.

What is the least Perfect Square Divisible by 20 and 40?

The least number divisible through 20 and also 40 = LCM(20, 40)LCM of 20 and 40 = 2 × 2 × 2 × 5 ⇒ the very least perfect square divisible by every 20 and 40 = LCM(20, 40) × 2 × 5 = 400 Therefore, 400 is the required number.

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What is the Relation in between GCF and also LCM the 20, 40?

The adhering to equation have the right to be offered to to express the relation between GCF and also LCM that 20 and also 40, i.e. GCF × LCM = 20 × 40.