LCM of 18 and also 24 is the smallest number among all widespread multiples of 18 and 24. The first few multiples of 18 and 24 are (18, 36, 54, 72, 90, 108, . . . ) and (24, 48, 72, 96, 120, 144, 168, . . . ) respectively. There are 3 frequently offered methods to discover LCM of 18 and also 24 - by listing multiples, by department technique, and also by prime factorization.

You are watching: Find the lcm of 18 and 24

1.LCM of 18 and 24
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 18 and 24 is 72.

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Explanation:

The LCM of 2 non-zero integers, x(18) and y(24), is the smallest positive integer m(72) that is divisible by both x(18) and also y(24) without any kind of remainder.


The techniques to uncover the LCM of 18 and 24 are explained listed below.

By Listing MultiplesBy Division MethodBy Prime Factorization Method

LCM of 18 and 24 by Listing Multiples

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To calculate the LCM of 18 and also 24 by listing out the prevalent multiples, we deserve to follow the given below steps:

Tip 1: List a few multiples of 18 (18, 36, 54, 72, 90, 108, . . . ) and also 24 (24, 48, 72, 96, 120, 144, 168, . . . . )Tip 2: The prevalent multiples from the multiples of 18 and also 24 are 72, 144, . . .Step 3: The smallest prevalent multiple of 18 and 24 is 72.

∴ The least common multiple of 18 and also 24 = 72.

LCM of 18 and 24 by Division Method

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To calculate the LCM of 18 and also 24 by the department strategy, we will divide the numbers(18, 24) by their prime determinants (preferably common). The product of these divisors gives the LCM of 18 and 24.

Tip 3: Continue the steps till only 1s are left in the last row.

The LCM of 18 and 24 is the product of all prime numbers on the left, i.e. LCM(18, 24) by department method = 2 × 2 × 2 × 3 × 3 = 72.

LCM of 18 and also 24 by Prime Factorization

Prime factorization of 18 and 24 is (2 × 3 × 3) = 21 × 32 and (2 × 2 × 2 × 3) = 23 × 31 respectively. LCM of 18 and 24 can be acquired by multiplying prime components raised to their respective highest possible power, i.e. 23 × 32 = 72.Hence, the LCM of 18 and 24 by prime factorization is 72.

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Example 2: Verify the relationship in between GCF and LCM of 18 and 24.

Solution:

The relation between GCF and also LCM of 18 and also 24 is given as,LCM(18, 24) × GCF(18, 24) = Product of 18, 24Prime factorization of 18 and also 24 is provided as, 18 = (2 × 3 × 3) = 21 × 32 and 24 = (2 × 2 × 2 × 3) = 23 × 31LCM(18, 24) = 72GCF(18, 24) = 6LHS = LCM(18, 24) × GCF(18, 24) = 72 × 6 = 432RHS = Product of 18, 24 = 18 × 24 = 432⇒ LHS = RHS = 432Hence, verified.


Example 3: The product of 2 numbers is 432. If their GCD is 6, what is their LCM?

Solution:

Given: GCD = 6product of numbers = 432∵ LCM × GCD = product of numbers⇒ LCM = Product/GCD = 432/6As such, the LCM is 72.The probable combicountry for the offered instance is LCM(18, 24) = 72.


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FAQs on LCM of 18 and also 24

What is the LCM of 18 and also 24?

The LCM of 18 and also 24 is 72. To uncover the LCM (least common multiple) of 18 and also 24, we have to uncover the multiples of 18 and also 24 (multiples of 18 = 18, 36, 54, 72; multiples of 24 = 24, 48, 72, 96) and also choose the smallest multiple that is precisely divisible by 18 and also 24, i.e., 72.

What is the Relation Between GCF and also LCM of 18, 24?

The following equation can be used to expush the relation between GCF and LCM of 18 and 24, i.e. GCF × LCM = 18 × 24.

What are the Methods to Find LCM of 18 and 24?

The generally supplied approaches to find the LCM of 18 and also 24 are:

Prime Factorization MethodDivision MethodListing Multiples

If the LCM of 24 and also 18 is 72, Find its GCF.

LCM(24, 18) × GCF(24, 18) = 24 × 18Due to the fact that the LCM of 24 and 18 = 72⇒ 72 × GCF(24, 18) = 432Because of this, the best widespread aspect = 432/72 = 6.

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Which of the following is the LCM of 18 and 24? 18, 5, 36, 72

The worth of LCM of 18, 24 is the smallest widespread multiple of 18 and also 24. The number satisfying the provided problem is 72.