LCM of 18 and 63

LCM of 18 and 63 is the smallest number among all common multiples of 18 and 63. The first few multiples of 18 and 63 are (18, 36, 54, 72, . . . ) and (63, 126, 189, 252, 315, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 63 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 18 and 63 is 126.

Explanation:

The LCM of two non-zero integers, x(18) and y(63), is the smallest positive integer m(126) that is divisible by both x(18) and y(63) without any remainder.

Let's look at the different methods for finding the LCM of 18 and 63.

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

LCM of 18 and 63 by Listing Multiples

To calculate the LCM of 18 and 63 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, . . . ) and 63 (63, 126, 189, 252, 315, . . . . )
• Step 2: The common multiples from the multiples of 18 and 63 are 126, 252, . . .
• Step 3: The smallest common multiple of 18 and 63 is 126.

∴ The least common multiple of 18 and 63 = 126.

LCM of 18 and 63 by Prime Factorization

Prime factorization of 18 and 63 is (2 × 3 × 3) = 2¹ × 3² and (3 × 3 × 7) = 3² × 7¹ respectively. LCM of 18 and 63 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 7¹ = 126.
Hence, the LCM of 18 and 63 by prime factorization is 126.

LCM of 18 and 63 by Division Method

To calculate the LCM of 18 and 63 by the division method, we will divide the numbers(18, 63) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 63.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 63. Write this prime number(2) on the left of the given numbers(18 and 63), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (18, 63) 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 63 is the product of all prime numbers on the left, i.e. LCM(18, 63) by division method = 2 × 3 × 3 × 7 = 126.

☛ Also Check:

• LCM of 8 and 28 - 56
• LCM of 5 and 10 - 10
• LCM of 120 and 180 - 360
• LCM of 12 and 48 - 48
• LCM of 19 and 57 - 57
• LCM of 63 and 105 - 315
• LCM of 12 and 16 - 48

FAQs on LCM of 18 and 63

What is the LCM of 18 and 63?

The LCM of 18 and 63 is 126. To find the LCM of 18 and 63, we need to find the multiples of 18 and 63 (multiples of 18 = 18, 36, 54, 72 . . . . 126; multiples of 63 = 63, 126, 189, 252) and choose the smallest multiple that is exactly divisible by 18 and 63, i.e., 126.

What are the Methods to Find LCM of 18 and 63?

The commonly used methods to find the LCM of 18 and 63 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

If the LCM of 63 and 18 is 126, Find its GCF.

LCM(63, 18) × GCF(63, 18) = 63 × 18
Since the LCM of 63 and 18 = 126
⇒ 126 × GCF(63, 18) = 1134
Therefore, the GCF (greatest common factor) = 1134/126 = 9.

Which of the following is the LCM of 18 and 63? 24, 42, 16, 126

The value of LCM of 18, 63 is the smallest common multiple of 18 and 63. The number satisfying the given condition is 126.

What is the Relation Between GCF and LCM of 18, 63?

The following equation can be used to express the relation between GCF and LCM of 18 and 63, i.e. GCF × LCM = 18 × 63.