LCM of 7 and 18

LCM of 7 and 18 is the smallest number among all common multiples of 7 and 18. The first few multiples of 7 and 18 are (7, 14, 21, 28, . . . ) and (18, 36, 54, 72, 90, 108, 126, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 18 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 7 and 18 is 126.

Explanation:

The LCM of two non-zero integers, x(7) and y(18), is the smallest positive integer m(126) that is divisible by both x(7) and y(18) without any remainder.

The methods to find the LCM of 7 and 18 are explained below.

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

LCM of 7 and 18 by Listing Multiples

To calculate the LCM of 7 and 18 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 7 (7, 14, 21, 28, . . . ) and 18 (18, 36, 54, 72, 90, 108, 126, . . . . )
• Step 2: The common multiples from the multiples of 7 and 18 are 126, 252, . . .
• Step 3: The smallest common multiple of 7 and 18 is 126.

∴ The least common multiple of 7 and 18 = 126.

LCM of 7 and 18 by Division Method

To calculate the LCM of 7 and 18 by the division method, we will divide the numbers(7, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 18.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 7 and 18. Write this prime number(2) on the left of the given numbers(7 and 18), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (7, 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 7 and 18 is the product of all prime numbers on the left, i.e. LCM(7, 18) by division method = 2 × 3 × 3 × 7 = 126.

LCM of 7 and 18 by Prime Factorization

Prime factorization of 7 and 18 is (7) = 7¹ and (2 × 3 × 3) = 2¹ × 3² respectively. LCM of 7 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 7¹ = 126.
Hence, the LCM of 7 and 18 by prime factorization is 126.

☛ Also Check:

• LCM of 63 and 105 - 315
• LCM of 8 and 12 - 24
• LCM of 60, 84 and 108 - 3780
• LCM of 15 and 60 - 60
• LCM of 30, 72 and 432 - 2160
• LCM of 4, 7 and 8 - 56
• LCM of 3, 4 and 8 - 24

FAQs on LCM of 7 and 18

What is the LCM of 7 and 18?

The LCM of 7 and 18 is 126. To find the LCM of 7 and 18, we need to find the multiples of 7 and 18 (multiples of 7 = 7, 14, 21, 28 . . . . 126; multiples of 18 = 18, 36, 54, 72 . . . . 126) and choose the smallest multiple that is exactly divisible by 7 and 18, i.e., 126.

What is the Least Perfect Square Divisible by 7 and 18?

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

If the LCM of 18 and 7 is 126, Find its GCF.

LCM(18, 7) × GCF(18, 7) = 18 × 7
Since the LCM of 18 and 7 = 126
⇒ 126 × GCF(18, 7) = 126
Therefore, the greatest common factor (GCF) = 126/126 = 1.

What are the Methods to Find LCM of 7 and 18?

The commonly used methods to find the LCM of 7 and 18 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

How to Find the LCM of 7 and 18 by Prime Factorization?

To find the LCM of 7 and 18 using prime factorization, we will find the prime factors, (7 = 7) and (18 = 2 × 3 × 3). LCM of 7 and 18 is the product of prime factors raised to their respective highest exponent among the numbers 7 and 18.
⇒ LCM of 7, 18 = 2¹ × 3² × 7¹ = 126.