LCM of 18 and 24 is the smallest number among all common 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 commonly used methods to find LCM of 18 and 24 - by listing multiples, by division method, and by prime factorization.

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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 two non-zero integers, x(18) and y(24), is the smallest positive integer m(72) that is divisible by both x(18) and y(24) without any remainder.


The methods to find the LCM of 18 and 24 are explained 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 24 by listing out the common multiples, we can follow the given below steps:

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

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

LCM of 18 and 24 by Division Method

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To calculate the LCM of 18 and 24 by the division method, we will divide the numbers(18, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 24.

Step 3: Continue the steps until 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 division method = 2 × 2 × 2 × 3 × 3 = 72.

LCM of 18 and 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 obtained by multiplying prime factors raised to their respective highest 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 between GCF and LCM of 18 and 24.

Solution:

The relation between GCF and LCM of 18 and 24 is given as,LCM(18, 24) × GCF(18, 24) = Product of 18, 24Prime factorization of 18 and 24 is given 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 two 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 = 432/6Therefore, the LCM is 72.The probable combination for the given case is LCM(18, 24) = 72.


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FAQs on LCM of 18 and 24

What is the LCM of 18 and 24?

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

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

The following equation can be used to express 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 commonly used methods to find the LCM of 18 and 24 are:

Prime Factorization MethodDivision MethodListing Multiples

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

LCM(24, 18) × GCF(24, 18) = 24 × 18Since the LCM of 24 and 18 = 72⇒ 72 × GCF(24, 18) = 432Therefore, the greatest common factor = 432/72 = 6.

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

The value of LCM of 18, 24 is the smallest common multiple of 18 and 24. The number satisfying the given condition is 72.