LCM of 45 and 63

LCM of 45 and 63 is the smallest number among all common multiples of 45 and 63. The first few multiples of 45 and 63 are (45, 90, 135, 180, . . . ) and (63, 126, 189, 252, 315, 378, . . . ) respectively. There are 3 commonly used methods to find LCM of 45 and 63 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 45 and 63 is 315.

Explanation:

The LCM of two non-zero integers, x(45) and y(63), is the smallest positive integer m(315) that is divisible by both x(45) and y(63) without any remainder.

The methods to find the LCM of 45 and 63 are explained below.

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

LCM of 45 and 63 by Listing Multiples

To calculate the LCM of 45 and 63 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 45 (45, 90, 135, 180, . . . ) and 63 (63, 126, 189, 252, 315, 378, . . . . )
• Step 2: The common multiples from the multiples of 45 and 63 are 315, 630, . . .
• Step 3: The smallest common multiple of 45 and 63 is 315.

∴ The least common multiple of 45 and 63 = 315.

LCM of 45 and 63 by Prime Factorization

Prime factorization of 45 and 63 is (3 × 3 × 5) = 3² × 5¹ and (3 × 3 × 7) = 3² × 7¹ respectively. LCM of 45 and 63 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 5¹ × 7¹ = 315.
Hence, the LCM of 45 and 63 by prime factorization is 315.

LCM of 45 and 63 by Division Method

To calculate the LCM of 45 and 63 by the division method, we will divide the numbers(45, 63) by their prime factors (preferably common). The product of these divisors gives the LCM of 45 and 63.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 45 and 63. Write this prime number(3) on the left of the given numbers(45 and 63), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (45, 63) is a multiple of 3, divide it by 3 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 45 and 63 is the product of all prime numbers on the left, i.e. LCM(45, 63) by division method = 3 × 3 × 5 × 7 = 315.

☛ Also Check:

• LCM of 9 and 12 - 36
• LCM of 2601 and 2616 - 2268072
• LCM of 4, 7 and 8 - 56
• LCM of 4, 12 and 20 - 60
• LCM of 6, 9 and 12 - 36
• LCM of 24 and 42 - 168
• LCM of 3 and 8 - 24

FAQs on LCM of 45 and 63

What is the LCM of 45 and 63?

The LCM of 45 and 63 is 315. To find the LCM of 45 and 63, we need to find the multiples of 45 and 63 (multiples of 45 = 45, 90, 135, 180 . . . . 315; multiples of 63 = 63, 126, 189, 252 . . . . 315) and choose the smallest multiple that is exactly divisible by 45 and 63, i.e., 315.

What is the Relation Between GCF and LCM of 45, 63?

The following equation can be used to express the relation between GCF and LCM of 45 and 63, i.e. GCF × LCM = 45 × 63.

How to Find the LCM of 45 and 63 by Prime Factorization?

To find the LCM of 45 and 63 using prime factorization, we will find the prime factors, (45 = 3 × 3 × 5) and (63 = 3 × 3 × 7). LCM of 45 and 63 is the product of prime factors raised to their respective highest exponent among the numbers 45 and 63.
⇒ LCM of 45, 63 = 3² × 5¹ × 7¹ = 315.

If the LCM of 63 and 45 is 315, Find its GCF.

LCM(63, 45) × GCF(63, 45) = 63 × 45
Since the LCM of 63 and 45 = 315
⇒ 315 × GCF(63, 45) = 2835
Therefore, the greatest common factor = 2835/315 = 9.

What is the Least Perfect Square Divisible by 45 and 63?

The least number divisible by 45 and 63 = LCM(45, 63)
LCM of 45 and 63 = 3 × 3 × 5 × 7 [Incomplete pair(s): 5, 7]
⇒ Least perfect square divisible by each 45 and 63 = LCM(45, 63) × 5 × 7 = 11025 [Square root of 11025 = √11025 = ±105]
Therefore, 11025 is the required number.