LCM of 18 and 28

LCM of 18 and 28 is the smallest number among all common multiples of 18 and 28. The first few multiples of 18 and 28 are (18, 36, 54, 72, 90, 108, 126, . . . ) and (28, 56, 84, 112, 140, 168, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 28 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 18 and 28 is 252.

Explanation:

The LCM of two non-zero integers, x(18) and y(28), is the smallest positive integer m(252) that is divisible by both x(18) and y(28) without any remainder.

Let's look at the different methods for finding the LCM of 18 and 28.

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

LCM of 18 and 28 by Listing Multiples

To calculate the LCM of 18 and 28 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, 126, . . . ) and 28 (28, 56, 84, 112, 140, 168, . . . . )
• Step 2: The common multiples from the multiples of 18 and 28 are 252, 504, . . .
• Step 3: The smallest common multiple of 18 and 28 is 252.

∴ The least common multiple of 18 and 28 = 252.

LCM of 18 and 28 by Prime Factorization

Prime factorization of 18 and 28 is (2 × 3 × 3) = 2¹ × 3² and (2 × 2 × 7) = 2² × 7¹ respectively. LCM of 18 and 28 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² × 7¹ = 252.
Hence, the LCM of 18 and 28 by prime factorization is 252.

LCM of 18 and 28 by Division Method

To calculate the LCM of 18 and 28 by the division method, we will divide the numbers(18, 28) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 28.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 28. Write this prime number(2) on the left of the given numbers(18 and 28), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (18, 28) 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 18 and 28 is the product of all prime numbers on the left, i.e. LCM(18, 28) by division method = 2 × 2 × 3 × 3 × 7 = 252.

☛ Also Check:

• LCM of 5 and 7 - 35
• LCM of 36 and 42 - 252
• LCM of 7 and 13 - 91
• LCM of 45 and 72 - 360
• LCM of 3, 4 and 5 - 60
• LCM of 18 and 24 - 72
• LCM of 3, 9 and 12 - 36

FAQs on LCM of 18 and 28

What is the LCM of 18 and 28?

The LCM of 18 and 28 is 252. To find the least common multiple of 18 and 28, we need to find the multiples of 18 and 28 (multiples of 18 = 18, 36, 54, 72 . . . . 252; multiples of 28 = 28, 56, 84, 112 . . . . 252) and choose the smallest multiple that is exactly divisible by 18 and 28, i.e., 252.

What is the Least Perfect Square Divisible by 18 and 28?

The least number divisible by 18 and 28 = LCM(18, 28)
LCM of 18 and 28 = 2 × 2 × 3 × 3 × 7 [Incomplete pair(s): 7]
⇒ Least perfect square divisible by each 18 and 28 = LCM(18, 28) × 7 = 1764 [Square root of 1764 = √1764 = ±42]
Therefore, 1764 is the required number.

If the LCM of 28 and 18 is 252, Find its GCF.

LCM(28, 18) × GCF(28, 18) = 28 × 18
Since the LCM of 28 and 18 = 252
⇒ 252 × GCF(28, 18) = 504
Therefore, the greatest common factor = 504/252 = 2.

What are the Methods to Find LCM of 18 and 28?

The commonly used methods to find the LCM of 18 and 28 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

What is the Relation Between GCF and LCM of 18, 28?

The following equation can be used to express the relation between GCF and LCM of 18 and 28, i.e. GCF × LCM = 18 × 28.