LCM of 12 and also 30 is the the smallest number amongst all typical multiples of 12 and also 30. The first couple of multiples that 12 and 30 room (12, 24, 36, 48, 60, 72, 84, . . . ) and (30, 60, 90, 120, . . . ) respectively. There are 3 frequently used techniques to discover LCM of 12 and also 30 - by division method, by prime factorization, and by listing multiples.

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

Answer: LCM the 12 and 30 is 60.

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Explanation:

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


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

By prime Factorization MethodBy Listing MultiplesBy department Method

LCM that 12 and 30 by prime Factorization

Prime administrate of 12 and also 30 is (2 × 2 × 3) = 22 × 31 and also (2 × 3 × 5) = 21 × 31 × 51 respectively. LCM the 12 and 30 deserve to be acquired by multiplying prime factors raised to their respective highest possible power, i.e. 22 × 31 × 51 = 60.Hence, the LCM that 12 and also 30 by element factorization is 60.

LCM the 12 and 30 by Listing Multiples

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To calculation the LCM of 12 and 30 by listing the end the usual multiples, we can follow the given listed below steps:

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

∴ The least usual multiple the 12 and also 30 = 60.

LCM the 12 and also 30 by department Method

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

Step 3: continue the procedures until only 1s space left in the critical row.

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

☛ additionally Check:


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

Solution:

The relation between GCF and also LCM the 12 and also 30 is given as,LCM(12, 30) × GCF(12, 30) = Product the 12, 30Prime administrate of 12 and 30 is offered 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: find the smallest number that is divisible by 12 and also 30 exactly.

Solution:

The smallest number the is divisible by 12 and 30 specifically is your LCM.⇒ Multiples the 12 and 30:

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

Therefore, the LCM of 12 and 30 is 60.


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FAQs on LCM that 12 and also 30

What is the LCM the 12 and 30?

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

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

The the very least number divisible through 12 and also 30 = LCM(12, 30)LCM of 12 and also 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 compelled number.

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

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

How to discover the LCM that 12 and 30 by prime Factorization?

To find the LCM of 12 and 30 using prime factorization, us will find the prime factors, (12 = 2 × 2 × 3) and (30 = 2 × 3 × 5). LCM the 12 and 30 is the product of prime components raised to your respective highest possible exponent among the number 12 and also 30.⇒ LCM that 12, 30 = 22 × 31 × 51 = 60.

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

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