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LCM of 45 and 99

LCM of 45 and 99 is the smallest number among all common multiples of 45 and 99. The first few multiples of 45 and 99 are (45, 90, 135, 180, 225, . . . ) and (99, 198, 297, 396, 495, . . . ) respectively. There are 3 commonly used methods to find LCM of 45 and 99 - by division method, by listing multiples, and by prime factorization.

1.	LCM of 45 and 99
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 45 and 99?

Answer: LCM of 45 and 99 is 495.

Explanation:

The LCM of two non-zero integers, x(45) and y(99), is the smallest positive integer m(495) that is divisible by both x(45) and y(99) without any remainder.

Methods to Find LCM of 45 and 99

Let's look at the different methods for finding the LCM of 45 and 99.

By Listing Multiples
By Division Method
By Prime Factorization Method

LCM of 45 and 99 by Listing Multiples

To calculate the LCM of 45 and 99 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, 225, . . . ) and 99 (99, 198, 297, 396, 495, . . . . )
Step 2: The common multiples from the multiples of 45 and 99 are 495, 990, . . .
Step 3: The smallest common multiple of 45 and 99 is 495.

∴ The least common multiple of 45 and 99 = 495.

LCM of 45 and 99 by Division Method

To calculate the LCM of 45 and 99 by the division method, we will divide the numbers(45, 99) by their prime factors (preferably common). The product of these divisors gives the LCM of 45 and 99.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 45 and 99. Write this prime number(3) on the left of the given numbers(45 and 99), separated as per the ladder arrangement.
Step 2: If any of the given numbers (45, 99) 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 99 is the product of all prime numbers on the left, i.e. LCM(45, 99) by division method = 3 × 3 × 5 × 11 = 495.

LCM of 45 and 99 by Prime Factorization

Prime factorization of 45 and 99 is (3 × 3 × 5) = 3² × 5¹ and (3 × 3 × 11) = 3² × 11¹ respectively. LCM of 45 and 99 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 5¹ × 11¹ = 495.
Hence, the LCM of 45 and 99 by prime factorization is 495.

☛ Also Check:

LCM of 45 and 99 Examples

Example 1: Verify the relationship between GCF and LCM of 45 and 99.

Solution:

The relation between GCF and LCM of 45 and 99 is given as,
LCM(45, 99) × GCF(45, 99) = Product of 45, 99
Prime factorization of 45 and 99 is given as, 45 = (3 × 3 × 5) = 3² × 5¹ and 99 = (3 × 3 × 11) = 3² × 11¹
LCM(45, 99) = 495
GCF(45, 99) = 9
LHS = LCM(45, 99) × GCF(45, 99) = 495 × 9 = 4455
RHS = Product of 45, 99 = 45 × 99 = 4455
⇒ LHS = RHS = 4455
Hence, verified.
Example 2: The GCD and LCM of two numbers are 9 and 495 respectively. If one number is 99, find the other number.

Solution:

Let the other number be y.
∵ GCD × LCM = 99 × y
⇒ y = (GCD × LCM)/99
⇒ y = (9 × 495)/99
⇒ y = 45
Therefore, the other number is 45.
Example 3: The product of two numbers is 4455. If their GCD is 9, what is their LCM?

Solution:

Given: GCD = 9
product of numbers = 4455
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 4455/9
Therefore, the LCM is 495.
The probable combination for the given case is LCM(45, 99) = 495.

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FAQs on LCM of 45 and 99

What is the LCM of 45 and 99?

The LCM of 45 and 99 is 495. To find the least common multiple of 45 and 99, we need to find the multiples of 45 and 99 (multiples of 45 = 45, 90, 135, 180 . . . . 495; multiples of 99 = 99, 198, 297, 396 . . . . 495) and choose the smallest multiple that is exactly divisible by 45 and 99, i.e., 495.

What is the Relation Between GCF and LCM of 45, 99?

The following equation can be used to express the relation between GCF and LCM of 45 and 99, i.e. GCF × LCM = 45 × 99.

If the LCM of 99 and 45 is 495, Find its GCF.

LCM(99, 45) × GCF(99, 45) = 99 × 45
Since the LCM of 99 and 45 = 495
⇒ 495 × GCF(99, 45) = 4455
Therefore, the GCF (greatest common factor) = 4455/495 = 9.

Which of the following is the LCM of 45 and 99? 11, 40, 28, 495

The value of LCM of 45, 99 is the smallest common multiple of 45 and 99. The number satisfying the given condition is 495.

What is the Least Perfect Square Divisible by 45 and 99?

The least number divisible by 45 and 99 = LCM(45, 99)
LCM of 45 and 99 = 3 × 3 × 5 × 11 [Incomplete pair(s): 5, 11]
⇒ Least perfect square divisible by each 45 and 99 = LCM(45, 99) × 5 × 11 = 27225 [Square root of 27225 = √27225 = ±165]
Therefore, 27225 is the required number.

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