LCM of 12 and also 30 is the the smallest number among all usual multiples of 12 and 30. The first few multiples that 12 and also 30 room (12, 24, 36, 48, 60, 72, 84, . . . ) and also (30, 60, 90, 120, . . . ) respectively. There space 3 commonly used techniques to uncover LCM of 12 and 30 - by division method, by prime factorization, and also by listing multiples.

You are watching: Whats the lcm of 12 and 30

1.LCM of 12 and 30
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM the 12 and also 30 is 60.

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Explanation:

The LCM of two non-zero integers, x(12) and also y(30), is the smallest hopeful integer m(60) that is divisible by both x(12) and y(30) without any type of remainder.


Let's look in ~ the various methods for finding the LCM that 12 and also 30.

By prime Factorization MethodBy Listing MultiplesBy division Method

LCM of 12 and 30 by prime Factorization

Prime administrate of 12 and 30 is (2 × 2 × 3) = 22 × 31 and (2 × 3 × 5) = 21 × 31 × 51 respectively. LCM the 12 and also 30 have the right to be obtained by multiply prime components raised to their respective highest power, i.e. 22 × 31 × 51 = 60.Hence, the LCM the 12 and also 30 by prime factorization is 60.

LCM the 12 and 30 by Listing Multiples

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To calculate the LCM of 12 and 30 through listing out the usual multiples, we have the right to follow the given below steps:

Step 1: list a couple of multiples that 12 (12, 24, 36, 48, 60, 72, 84, . . . ) and 30 (30, 60, 90, 120, . . . . )Step 2: The usual multiples from the multiples that 12 and also 30 room 60, 120, . . .Step 3: The smallest usual multiple the 12 and 30 is 60.

∴ The least typical multiple that 12 and also 30 = 60.

LCM of 12 and also 30 by division Method

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To calculation the LCM the 12 and 30 through the division method, we will divide the numbers(12, 30) by your prime components (preferably common). The product of this divisors provides the LCM of 12 and 30.

Step 3: continue the actions until only 1s space left in the last row.

The LCM of 12 and 30 is the product of all prime number on the left, i.e. LCM(12, 30) by division method = 2 × 2 × 3 × 5 = 60.

☛ likewise Check:


Example 2: Verify the relationship in between GCF and LCM of 12 and also 30.

Solution:

The relation between GCF and also LCM that 12 and also 30 is provided as,LCM(12, 30) × GCF(12, 30) = Product that 12, 30Prime administrate of 12 and 30 is provided as, 12 = (2 × 2 × 3) = 22 × 31 and also 30 = (2 × 3 × 5) = 21 × 31 × 51LCM(12, 30) = 60GCF(12, 30) = 6LHS = LCM(12, 30) × GCF(12, 30) = 60 × 6 = 360RHS = Product the 12, 30 = 12 × 30 = 360⇒ LHS = RHS = 360Hence, verified.


Example 3: discover the the smallest number that is divisible by 12 and 30 exactly.

Solution:

The the smallest number that is divisible by 12 and 30 exactly is their LCM.⇒ Multiples of 12 and also 30:

Multiples that 12 = 12, 24, 36, 48, 60, 72, . . . .Multiples that 30 = 30, 60, 90, 120, 150, 180, . . . .

Therefore, the LCM that 12 and also 30 is 60.


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FAQs on LCM that 12 and 30

What is the LCM that 12 and 30?

The LCM of 12 and 30 is 60. To discover the LCM the 12 and 30, we need to uncover the multiples of 12 and 30 (multiples that 12 = 12, 24, 36, 48 . . . . 60; multiples that 30 = 30, 60, 90, 120) and choose the smallest multiple the is exactly divisible through 12 and also 30, i.e., 60.

What is the least Perfect Square Divisible by 12 and also 30?

The the very least number divisible through 12 and also 30 = LCM(12, 30)LCM of 12 and 30 = 2 × 2 × 3 × 5 ⇒ the very least perfect square divisible by every 12 and also 30 = LCM(12, 30) × 3 × 5 = 900 Therefore, 900 is the forced number.

What is the Relation between GCF and also LCM that 12, 30?

The following equation can be provided to to express the relation between GCF and also LCM the 12 and 30, i.e. GCF × LCM = 12 × 30.

How to find the LCM of 12 and also 30 by element Factorization?

To uncover the LCM of 12 and 30 utilizing prime factorization, we will discover the prime factors, (12 = 2 × 2 × 3) and (30 = 2 × 3 × 5). LCM the 12 and also 30 is the product of prime determinants raised to their respective greatest exponent amongst the number 12 and also 30.⇒ LCM the 12, 30 = 22 × 31 × 51 = 60.

If the LCM that 30 and 12 is 60, uncover its GCF.

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LCM(30, 12) × GCF(30, 12) = 30 × 12Since the LCM the 30 and 12 = 60⇒ 60 × GCF(30, 12) = 360Therefore, the greatest typical factor (GCF) = 360/60 = 6.