LCM of 45 and 63

LCM of 45 and 63 is 315. The least common multiple of any two or more natural numbers is the number that is the lowest of their common multiples. For better learning of the concepts, students can refer to the article HCF and LCM developed by experts in simple language. The detailed explanation provided in this article helps students calculate the HCF and LCM of given numbers in an efficient manner. In this article, we will discuss how to find the least common multiple of 45 and 63.

What is LCM of 45 and 63?

The Least Common Multiple of 45 and 63 is 315.

lcm of 45 and 63

How to Find LCM of 45 and 63?

We can obtain the LCM of 45 and 63 by using three methods:

  • Prime Factorisation
  • Division method
  • Listing the Multiples

LCM of 45 and 63 Using Prime Factorisation Method

In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 45 and 63 can be denoted as;

45 = 3 × 3 × 5

63 = 3 × 3 × 7

LCM (45, 63) = 3 × 3 × 5 × 7 = 315

LCM of 45 and 63 Using Division Method

In the division method, we divide the numbers 45 and 63 by their prime factors until we get the result as one in the complete row. The product of these divisors denotes the least common multiple of 45 and 63.

3 45 63
3 15 21
5 5 7
7 1 7
x 1 1

No further division can be done.

Therefore, LCM (45, 63) = 3 × 3 × 5 × 7 = 315

LCM of 45 and 63 Using Listing the Multiples

Here, we list down the multiples of given natural numbers to calculate the lowest common multiple among them. The below table represents the multiples of 45 and 63.

Multiples of 45 Multiples of 63
45 63
90 126
135 189
180 252
225 315
270 378
315 441
360 504

LCM (45, 63) = 315

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Solved Examples

1. What is the smallest number that is divisible by both 45 and 63?

Solution: 315 is the smallest number that is divisible by both 45 and 63. 

2. The GCD and LCM of the two numbers are 9 and 315. If one number is 63, calculate the other number.

Solution: Let the other number be p

We know that,

GCD × LCM = 63 × p

p = (GCD × LCM) / 63

p = (9 × 315) / 63

p = 45

Hence the other number is 45.

Frequently Asked Questions on LCM of 45 and 63

Q1

What is the LCM of 45 and 63?

The LCM of 45 and 63 is 315.
Q2

What are the methods used to find the LCM of 45 and 63?

The following methods are used to find the LCM of 45 and 63:

Prime Factorisation

Division Method

Listing the Multiples

Q3

Which of the following is the highest common factor of 45 and 63? 10, 19, 11, 9

9 is the highest common factor of 45 and 63.
Q4

Find the GCF if the LCM of 45 and 63 is 315.

GCF × LCM = 45 × 63

Given

LCM = 315

GCF × 315 = 45 × 63

GCF = 9

Q5

Mention the LCM of 45 and 63 and the HCF of 45 and 63.

The LCM of 45 and 63 is 315 and the HCF of 45 and 63 is 9.

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