LCM of 4 and 18

LCM of 4 and 18 is the smallest number among all common multiples of 4 and 18. The first few multiples of 4 and 18 are (4, 8, 12, 16, 20, . . . ) and (18, 36, 54, 72, 90, 108, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 18 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 4 and 18 is 36.

Explanation:

The LCM of two non-zero integers, x(4) and y(18), is the smallest positive integer m(36) that is divisible by both x(4) and y(18) without any remainder.

The methods to find the LCM of 4 and 18 are explained below.

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

LCM of 4 and 18 by Prime Factorization

Prime factorization of 4 and 18 is (2 × 2) = 2² and (2 × 3 × 3) = 2¹ × 3² respectively. LCM of 4 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² = 36.
Hence, the LCM of 4 and 18 by prime factorization is 36.

LCM of 4 and 18 by Listing Multiples

To calculate the LCM of 4 and 18 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 4 (4, 8, 12, 16, 20, . . . ) and 18 (18, 36, 54, 72, 90, 108, . . . . )
• Step 2: The common multiples from the multiples of 4 and 18 are 36, 72, . . .
• Step 3: The smallest common multiple of 4 and 18 is 36.

∴ The least common multiple of 4 and 18 = 36.

LCM of 4 and 18 by Division Method

To calculate the LCM of 4 and 18 by the division method, we will divide the numbers(4, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 18.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 18. Write this prime number(2) on the left of the given numbers(4 and 18), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (4, 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 4 and 18 is the product of all prime numbers on the left, i.e. LCM(4, 18) by division method = 2 × 2 × 3 × 3 = 36.

☛ Also Check:

• LCM of 7 and 21 - 21
• LCM of 3, 6 and 7 - 42
• LCM of 4, 9 and 10 - 180
• LCM of 14 and 122 - 854
• LCM of 4, 6 and 12 - 12
• LCM of 7 and 35 - 35
• LCM of 30, 72 and 432 - 2160

FAQs on LCM of 4 and 18

What is the LCM of 4 and 18?

The LCM of 4 and 18 is 36. To find the LCM (least common multiple) of 4 and 18, we need to find the multiples of 4 and 18 (multiples of 4 = 4, 8, 12, 16 . . . . 36; multiples of 18 = 18, 36, 54, 72) and choose the smallest multiple that is exactly divisible by 4 and 18, i.e., 36.

What are the Methods to Find LCM of 4 and 18?

The commonly used methods to find the LCM of 4 and 18 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

If the LCM of 18 and 4 is 36, Find its GCF.

LCM(18, 4) × GCF(18, 4) = 18 × 4
Since the LCM of 18 and 4 = 36
⇒ 36 × GCF(18, 4) = 72
Therefore, the GCF = 72/36 = 2.

Which of the following is the LCM of 4 and 18? 45, 36, 42, 2

The value of LCM of 4, 18 is the smallest common multiple of 4 and 18. The number satisfying the given condition is 36.

How to Find the LCM of 4 and 18 by Prime Factorization?

To find the LCM of 4 and 18 using prime factorization, we will find the prime factors, (4 = 2 × 2) and (18 = 2 × 3 × 3). LCM of 4 and 18 is the product of prime factors raised to their respective highest exponent among the numbers 4 and 18.
⇒ LCM of 4, 18 = 2² × 3² = 36.