LCM that 12 and also 21 is the smallest number amongst all usual multiples the 12 and 21. The first few multiples of 12 and 21 are (12, 24, 36, 48, . . . ) and (21, 42, 63, 84, 105, . . . ) respectively. There are 3 frequently used methods to discover LCM that 12 and also 21 - by department method, by listing multiples, and also by element factorization.

You are watching: What is the lowest common multiple of 12 and 21

1.LCM that 12 and 21
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM of 12 and 21 is 84.

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Explanation:

The LCM of 2 non-zero integers, x(12) and also y(21), is the smallest positive integer m(84) the is divisible by both x(12) and y(21) without any remainder.


Let's look in ~ the various methods because that finding the LCM that 12 and also 21.

By division MethodBy element Factorization MethodBy Listing Multiples

LCM of 12 and also 21 by division Method

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To calculate the LCM the 12 and also 21 through the department method, we will certainly divide the numbers(12, 21) by their prime factors (preferably common). The product of this divisors gives the LCM the 12 and also 21.

Step 3: proceed the steps until just 1s are left in the last row.

The LCM the 12 and also 21 is the product of every prime number on the left, i.e. LCM(12, 21) by division method = 2 × 2 × 3 × 7 = 84.

LCM of 12 and also 21 by element Factorization

Prime administrate of 12 and 21 is (2 × 2 × 3) = 22 × 31 and also (3 × 7) = 31 × 71 respectively. LCM of 12 and also 21 have the right to be obtained by multiply prime determinants raised to your respective highest power, i.e. 22 × 31 × 71 = 84.Hence, the LCM of 12 and also 21 by prime factorization is 84.

LCM the 12 and 21 through Listing Multiples

To calculation the LCM of 12 and also 21 by listing the end the common multiples, we can follow the given below steps:

Step 1: list a couple of multiples that 12 (12, 24, 36, 48, . . . ) and 21 (21, 42, 63, 84, 105, . . . . )Step 2: The usual multiples from the multiples that 12 and 21 are 84, 168, . . .Step 3: The smallest common multiple of 12 and 21 is 84.

∴ The least common multiple of 12 and also 21 = 84.

☛ also Check:


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FAQs on LCM of 12 and also 21

What is the LCM of 12 and also 21?

The LCM the 12 and 21 is 84. To uncover the LCM (least usual multiple) that 12 and also 21, we need to discover the multiples the 12 and 21 (multiples of 12 = 12, 24, 36, 48 . . . . 84; multiples of 21 = 21, 42, 63, 84) and also choose the smallest multiple the is precisely divisible by 12 and also 21, i.e., 84.

How to uncover the LCM of 12 and 21 by element Factorization?

To uncover the LCM of 12 and also 21 using prime factorization, we will uncover the element factors, (12 = 2 × 2 × 3) and also (21 = 3 × 7). LCM that 12 and 21 is the product of prime factors raised to their respective highest possible exponent amongst the numbers 12 and also 21.⇒ LCM that 12, 21 = 22 × 31 × 71 = 84.

If the LCM of 21 and 12 is 84, find its GCF.

LCM(21, 12) × GCF(21, 12) = 21 × 12Since the LCM the 21 and also 12 = 84⇒ 84 × GCF(21, 12) = 252Therefore, the GCF (greatest common factor) = 252/84 = 3.

Which the the adhering to is the LCM the 12 and also 21? 21, 12, 36, 84

The worth of LCM that 12, 21 is the smallest typical multiple of 12 and 21. The number satisfying the given condition is 84.

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What is the Relation between GCF and also LCM the 12, 21?

The complying with equation can be supplied to refer the relation in between GCF and LCM the 12 and also 21, i.e. GCF × LCM = 12 × 21.