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LCM of 10 and 18

LCM of 10 and 18 is the smallest number among all common multiples of 10 and 18. The first few multiples of 10 and 18 are (10, 20, 30, 40, 50, . . . ) and (18, 36, 54, 72, 90, 108, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 18 - by prime factorization, by division method, and by listing multiples.

1.	LCM of 10 and 18
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 10 and 18?

Answer: LCM of 10 and 18 is 90.

Explanation:

The LCM of two non-zero integers, x(10) and y(18), is the smallest positive integer m(90) that is divisible by both x(10) and y(18) without any remainder.

Methods to Find LCM of 10 and 18

Let's look at the different methods for finding the LCM of 10 and 18.

By Listing Multiples
By Prime Factorization Method
By Division Method

LCM of 10 and 18 by Listing Multiples

To calculate the LCM of 10 and 18 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 10 (10, 20, 30, 40, 50, . . . ) and 18 (18, 36, 54, 72, 90, 108, . . . . )
Step 2: The common multiples from the multiples of 10 and 18 are 90, 180, . . .
Step 3: The smallest common multiple of 10 and 18 is 90.

∴ The least common multiple of 10 and 18 = 90.

LCM of 10 and 18 by Prime Factorization

Prime factorization of 10 and 18 is (2 × 5) = 2¹ × 5¹ and (2 × 3 × 3) = 2¹ × 3² respectively. LCM of 10 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 5¹ = 90.
Hence, the LCM of 10 and 18 by prime factorization is 90.

LCM of 10 and 18 by Division Method

To calculate the LCM of 10 and 18 by the division method, we will divide the numbers(10, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 18.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 18. Write this prime number(2) on the left of the given numbers(10 and 18), separated as per the ladder arrangement.
Step 2: If any of the given numbers (10, 18) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 10 and 18 is the product of all prime numbers on the left, i.e. LCM(10, 18) by division method = 2 × 3 × 3 × 5 = 90.

☛ Also Check:

LCM of 10 and 18 Examples

Example 1: The product of two numbers is 180. If their GCD is 2, what is their LCM?

Solution:

Given: GCD = 2
product of numbers = 180
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 180/2
Therefore, the LCM is 90.
The probable combination for the given case is LCM(10, 18) = 90.
Example 2: Verify the relationship between GCF and LCM of 10 and 18.

Solution:

The relation between GCF and LCM of 10 and 18 is given as,
LCM(10, 18) × GCF(10, 18) = Product of 10, 18
Prime factorization of 10 and 18 is given as, 10 = (2 × 5) = 2¹ × 5¹ and 18 = (2 × 3 × 3) = 2¹ × 3²
LCM(10, 18) = 90
GCF(10, 18) = 2
LHS = LCM(10, 18) × GCF(10, 18) = 90 × 2 = 180
RHS = Product of 10, 18 = 10 × 18 = 180
⇒ LHS = RHS = 180
Hence, verified.
Example 3: The GCD and LCM of two numbers are 2 and 90 respectively. If one number is 18, find the other number.

Solution:

Let the other number be p.
∵ GCD × LCM = 18 × p
⇒ p = (GCD × LCM)/18
⇒ p = (2 × 90)/18
⇒ p = 10
Therefore, the other number is 10.

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FAQs on LCM of 10 and 18

What is the LCM of 10 and 18?

The LCM of 10 and 18 is 90. To find the LCM of 10 and 18, we need to find the multiples of 10 and 18 (multiples of 10 = 10, 20, 30, 40 . . . . 90; multiples of 18 = 18, 36, 54, 72 . . . . 90) and choose the smallest multiple that is exactly divisible by 10 and 18, i.e., 90.

What are the Methods to Find LCM of 10 and 18?

The commonly used methods to find the LCM of 10 and 18 are:

Listing Multiples
Division Method
Prime Factorization Method

What is the Relation Between GCF and LCM of 10, 18?

The following equation can be used to express the relation between GCF and LCM of 10 and 18, i.e. GCF × LCM = 10 × 18.

Which of the following is the LCM of 10 and 18? 28, 50, 90, 12

The value of LCM of 10, 18 is the smallest common multiple of 10 and 18. The number satisfying the given condition is 90.

If the LCM of 18 and 10 is 90, Find its GCF.

LCM(18, 10) × GCF(18, 10) = 18 × 10
Since the LCM of 18 and 10 = 90
⇒ 90 × GCF(18, 10) = 180
Therefore, the GCF = 180/90 = 2.

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