A day full of math games & activities. Find one near you.

LCM of 63 and 105

LCM of 63 and 105 is the smallest number among all common multiples of 63 and 105. The first few multiples of 63 and 105 are (63, 126, 189, 252, 315, . . . ) and (105, 210, 315, 420, 525, 630, 735, . . . ) respectively. There are 3 commonly used methods to find LCM of 63 and 105 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 63 and 105
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 63 and 105?

Answer: LCM of 63 and 105 is 315.

Explanation:

The LCM of two non-zero integers, x(63) and y(105), is the smallest positive integer m(315) that is divisible by both x(63) and y(105) without any remainder.

Methods to Find LCM of 63 and 105

The methods to find the LCM of 63 and 105 are explained below.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 63 and 105 by Division Method

To calculate the LCM of 63 and 105 by the division method, we will divide the numbers(63, 105) by their prime factors (preferably common). The product of these divisors gives the LCM of 63 and 105.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 63 and 105. Write this prime number(3) on the left of the given numbers(63 and 105), separated as per the ladder arrangement.
Step 2: If any of the given numbers (63, 105) 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 63 and 105 is the product of all prime numbers on the left, i.e. LCM(63, 105) by division method = 3 × 3 × 5 × 7 = 315.

LCM of 63 and 105 by Prime Factorization

Prime factorization of 63 and 105 is (3 × 3 × 7) = 3² × 7¹ and (3 × 5 × 7) = 3¹ × 5¹ × 7¹ respectively. LCM of 63 and 105 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 5¹ × 7¹ = 315.
Hence, the LCM of 63 and 105 by prime factorization is 315.

LCM of 63 and 105 by Listing Multiples

To calculate the LCM of 63 and 105 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 63 (63, 126, 189, 252, 315, . . . ) and 105 (105, 210, 315, 420, 525, 630, 735, . . . . )
Step 2: The common multiples from the multiples of 63 and 105 are 315, 630, . . .
Step 3: The smallest common multiple of 63 and 105 is 315.

∴ The least common multiple of 63 and 105 = 315.

☛ Also Check:

LCM of 63 and 105 Examples

Example 1: The product of two numbers is 6615. If their GCD is 21, what is their LCM?

Solution:

Given: GCD = 21
product of numbers = 6615
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 6615/21
Therefore, the LCM is 315.
The probable combination for the given case is LCM(63, 105) = 315.
Example 2: Verify the relationship between GCF and LCM of 63 and 105.

Solution:

The relation between GCF and LCM of 63 and 105 is given as,
LCM(63, 105) × GCF(63, 105) = Product of 63, 105
Prime factorization of 63 and 105 is given as, 63 = (3 × 3 × 7) = 3² × 7¹ and 105 = (3 × 5 × 7) = 3¹ × 5¹ × 7¹
LCM(63, 105) = 315
GCF(63, 105) = 21
LHS = LCM(63, 105) × GCF(63, 105) = 315 × 21 = 6615
RHS = Product of 63, 105 = 63 × 105 = 6615
⇒ LHS = RHS = 6615
Hence, verified.
Example 3: Find the smallest number that is divisible by 63 and 105 exactly.

Solution:

The smallest number that is divisible by 63 and 105 exactly is their LCM.
⇒ Multiples of 63 and 105:
- Multiples of 63 = 63, 126, 189, 252, 315, . . . .
- Multiples of 105 = 105, 210, 315, 420, 525, . . . .
Therefore, the LCM of 63 and 105 is 315.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on LCM of 63 and 105

What is the LCM of 63 and 105?

The LCM of 63 and 105 is 315. To find the least common multiple (LCM) of 63 and 105, we need to find the multiples of 63 and 105 (multiples of 63 = 63, 126, 189, 252 . . . . 315; multiples of 105 = 105, 210, 315, 420) and choose the smallest multiple that is exactly divisible by 63 and 105, i.e., 315.

If the LCM of 105 and 63 is 315, Find its GCF.

LCM(105, 63) × GCF(105, 63) = 105 × 63
Since the LCM of 105 and 63 = 315
⇒ 315 × GCF(105, 63) = 6615
Therefore, the GCF (greatest common factor) = 6615/315 = 21.

How to Find the LCM of 63 and 105 by Prime Factorization?

To find the LCM of 63 and 105 using prime factorization, we will find the prime factors, (63 = 3 × 3 × 7) and (105 = 3 × 5 × 7). LCM of 63 and 105 is the product of prime factors raised to their respective highest exponent among the numbers 63 and 105.
⇒ LCM of 63, 105 = 3² × 5¹ × 7¹ = 315.

What is the Relation Between GCF and LCM of 63, 105?

The following equation can be used to express the relation between GCF and LCM of 63 and 105, i.e. GCF × LCM = 63 × 105.

What is the Least Perfect Square Divisible by 63 and 105?

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

Download FREE Study Materials

LCM and GCF

Math worksheets and
visual curriculum