LCM the 40 and also 60 is the the smallest number among all usual multiples that 40 and 60. The first few multiples the 40 and 60 space (40, 80, 120, 160, . . . ) and (60, 120, 180, 240, . . . ) respectively. There room 3 typically used approaches to discover LCM that 40 and 60 - through listing multiples, by element factorization, and by division method.

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1.LCM of 40 and also 60
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM that 40 and also 60 is 120.

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Explanation:

The LCM of 2 non-zero integers, x(40) and y(60), is the smallest optimistic integer m(120) that is divisible by both x(40) and y(60) without any kind of remainder.


The approaches to find the LCM that 40 and 60 are described below.

By Listing MultiplesBy element Factorization MethodBy division Method

LCM that 40 and also 60 through Listing Multiples

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To calculate the LCM that 40 and also 60 by listing out the usual multiples, we deserve to follow the given below steps:

Step 1: list a few multiples that 40 (40, 80, 120, 160, . . . ) and also 60 (60, 120, 180, 240, . . . . )Step 2: The common multiples indigenous the multiples of 40 and also 60 are 120, 240, . . .Step 3: The smallest typical multiple of 40 and 60 is 120.

∴ The least common multiple that 40 and also 60 = 120.

LCM of 40 and 60 by prime Factorization

Prime factorization of 40 and 60 is (2 × 2 × 2 × 5) = 23 × 51 and also (2 × 2 × 3 × 5) = 22 × 31 × 51 respectively. LCM the 40 and also 60 have the right to be acquired by multiplying prime determinants raised to their respective highest possible power, i.e. 23 × 31 × 51 = 120.Hence, the LCM of 40 and also 60 by prime factorization is 120.

LCM of 40 and also 60 by division Method

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To calculate the LCM that 40 and also 60 through the department method, we will divide the numbers(40, 60) by their prime factors (preferably common). The product of these divisors gives the LCM the 40 and 60.

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

The LCM the 40 and 60 is the product of all prime numbers on the left, i.e. LCM(40, 60) by department method = 2 × 2 × 2 × 3 × 5 = 120.

☛ additionally Check:


Example 2: Verify the relationship in between GCF and LCM the 40 and also 60.

Solution:

The relation in between GCF and LCM of 40 and 60 is provided as,LCM(40, 60) × GCF(40, 60) = Product that 40, 60Prime administer of 40 and also 60 is provided as, 40 = (2 × 2 × 2 × 5) = 23 × 51 and also 60 = (2 × 2 × 3 × 5) = 22 × 31 × 51LCM(40, 60) = 120GCF(40, 60) = 20LHS = LCM(40, 60) × GCF(40, 60) = 120 × 20 = 2400RHS = Product of 40, 60 = 40 × 60 = 2400⇒ LHS = RHS = 2400Hence, verified.


Example 3: find the the smallest number the is divisible by 40 and 60 exactly.

Solution:

The smallest number the is divisible through 40 and also 60 precisely is their LCM.⇒ Multiples the 40 and 60:

Multiples of 40 = 40, 80, 120, 160, 200, . . . .Multiples that 60 = 60, 120, 180, 240, 300, . . . .

Therefore, the LCM of 40 and also 60 is 120.


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FAQs ~ above LCM that 40 and also 60

What is the LCM the 40 and 60?

The LCM that 40 and also 60 is 120. To discover the least typical multiple (LCM) the 40 and also 60, we need to find the multiples that 40 and also 60 (multiples that 40 = 40, 80, 120, 160; multiples the 60 = 60, 120, 180, 240) and also choose the smallest multiple the is precisely divisible through 40 and 60, i.e., 120.

What is the Relation between GCF and also LCM the 40, 60?

The following equation can be used to to express the relation in between GCF and LCM that 40 and 60, i.e. GCF × LCM = 40 × 60.

What room the techniques to discover LCM of 40 and also 60?

The typically used methods to uncover the LCM the 40 and 60 are:

Division MethodListing MultiplesPrime administrate Method

What is the least Perfect Square Divisible by 40 and also 60?

The least number divisible by 40 and 60 = LCM(40, 60)LCM the 40 and 60 = 2 × 2 × 2 × 3 × 5 ⇒ least perfect square divisible by every 40 and 60 = LCM(40, 60) × 2 × 3 × 5 = 3600 Therefore, 3600 is the forced number.

If the LCM of 60 and 40 is 120, discover its GCF.

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LCM(60, 40) × GCF(60, 40) = 60 × 40Since the LCM the 60 and 40 = 120⇒ 120 × GCF(60, 40) = 2400Therefore, the greatest usual factor (GCF) = 2400/120 = 20.