What Is the Lcm of 3 and 18

LCM of 3 and 18

LCM of 3 and 18 is the smallest number among all common multiples of 3 and 18. The first few multiples of 3 and 18 are (3, 6, 9, 12, 15, . . . ) and (18, 36, 54, 72, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 18 - by listing multiples, by division method, and by prime factorization.

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

What is the LCM of 3 and 18?

Answer: LCM of 3 and 18 is 18.

Explanation:

The LCM of two non-zero integers, x(3) and y(18), is the smallest positive integer m(18) that is divisible by both x(3) and y(18) without any remainder.

Methods to Find LCM of 3 and 18

Let's look at the different methods for finding the LCM of 3 and 18.

• By Division Method
• By Prime Factorization Method
• By Listing Multiples

LCM of 3 and 18 by Division Method

To calculate the LCM of 3 and 18 by the division method, we will divide the numbers(3, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 18.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3 and 18. Write this prime number(2) on the left of the given numbers(3 and 18), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (3, 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 3 and 18 is the product of all prime numbers on the left, i.e. LCM(3, 18) by division method = 2 × 3 × 3 = 18.

LCM of 3 and 18 by Prime Factorization

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

LCM of 3 and 18 by Listing Multiples

To calculate the LCM of 3 and 18 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 3 (3, 6, 9, 12, 15, . . . ) and 18 (18, 36, 54, 72, . . . . )
• Step 2: The common multiples from the multiples of 3 and 18 are 18, 36, . . .
• Step 3: The smallest common multiple of 3 and 18 is 18.

∴ The least common multiple of 3 and 18 = 18.

☛ Also Check:

• LCM of 30 and 75 - 150
• LCM of 36 and 42 - 252
• LCM of 20, 30 and 40 - 120
• LCM of 4 and 9 - 36
• LCM of 16 and 36 - 144
• LCM of 10 and 20 - 20
• LCM of 16, 24 and 36 - 144

FAQs on LCM of 3 and 18

What is the LCM of 3 and 18?

The LCM of 3 and 18 is 18 . To find the least common multiple (LCM) of 3 and 18, we need to find the multiples of 3 and 18 (multiples of 3 = 3, 6, 9, 12 . . . . 18; multiples of 18 = 18, 36, 54, 72) and choose the smallest multiple that is exactly divisible by 3 and 18, i.e., 18.

What is the Relation Between GCF and LCM of 3, 18?

The following equation can be used to express the relation between GCF and LCM of 3 and 18, i.e. GCF × LCM = 3 × 18.

If the LCM of 18 and 3 is 18, Find its GCF.

LCM(18, 3) × GCF(18, 3) = 18 × 3
Since the LCM of 18 and 3 = 18
⇒ 18 × GCF(18, 3) = 54
Therefore, the greatest common factor = 54/18 = 3.

Which of the following is the LCM of 3 and 18? 18, 11, 36, 32

The value of LCM of 3, 18 is the smallest common multiple of 3 and 18. The number satisfying the given condition is 18.

How to Find the LCM of 3 and 18 by Prime Factorization?

To find the LCM of 3 and 18 using prime factorization, we will find the prime factors, (3 = 3) and (18 = 2 × 3 × 3). LCM of 3 and 18 is the product of prime factors raised to their respective highest exponent among the numbers 3 and 18.
⇒ LCM of 3, 18 = 2¹ × 3² = 18.

What Is the Lcm of 3 and 18

Source: https://www.cuemath.com/numbers/lcm-of-3-and-18/

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