LCM of 9 and 45

LCM of 9 and 45 is the smallest number among all common multiples of 9 and 45. The first few multiples of 9 and 45 are (9, 18, 27, 36, 45, 54, 63, . . . ) and (45, 90, 135, 180, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 45 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 9 and 45 is 45.

Explanation:

The LCM of two non-zero integers, x(9) and y(45), is the smallest positive integer m(45) that is divisible by both x(9) and y(45) without any remainder.

Let's look at the different methods for finding the LCM of 9 and 45.

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

LCM of 9 and 45 by Listing Multiples

To calculate the LCM of 9 and 45 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 9 (9, 18, 27, 36, 45, 54, 63, . . . ) and 45 (45, 90, 135, 180, . . . . )
• Step 2: The common multiples from the multiples of 9 and 45 are 45, 90, . . .
• Step 3: The smallest common multiple of 9 and 45 is 45.

∴ The least common multiple of 9 and 45 = 45.

LCM of 9 and 45 by Division Method

To calculate the LCM of 9 and 45 by the division method, we will divide the numbers(9, 45) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 45.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 45. Write this prime number(3) on the left of the given numbers(9 and 45), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (9, 45) 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 9 and 45 is the product of all prime numbers on the left, i.e. LCM(9, 45) by division method = 3 × 3 × 5 = 45.

LCM of 9 and 45 by Prime Factorization

Prime factorization of 9 and 45 is (3 × 3) = 3² and (3 × 3 × 5) = 3² × 5¹ respectively. LCM of 9 and 45 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 5¹ = 45.
Hence, the LCM of 9 and 45 by prime factorization is 45.

☛ Also Check:

• LCM of 16 and 48 - 48
• LCM of 16 and 24 - 48
• LCM of 45, 60 and 75 - 900
• LCM of 6 and 20 - 60
• LCM of 75 and 80 - 1200
• LCM of 18 and 40 - 360
• LCM of 8 and 64 - 64

FAQs on LCM of 9 and 45

What is the LCM of 9 and 45?

The LCM of 9 and 45 is 45. To find the LCM (least common multiple) of 9 and 45, we need to find the multiples of 9 and 45 (multiples of 9 = 9, 18, 27, 36 . . . . 45; multiples of 45 = 45, 90, 135, 180) and choose the smallest multiple that is exactly divisible by 9 and 45, i.e., 45.

Which of the following is the LCM of 9 and 45? 45, 30, 28, 18

The value of LCM of 9, 45 is the smallest common multiple of 9 and 45. The number satisfying the given condition is 45.

How to Find the LCM of 9 and 45 by Prime Factorization?

To find the LCM of 9 and 45 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (45 = 3 × 3 × 5). LCM of 9 and 45 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 45.
⇒ LCM of 9, 45 = 3² × 5¹ = 45.

What is the Relation Between GCF and LCM of 9, 45?

The following equation can be used to express the relation between GCF and LCM of 9 and 45, i.e. GCF × LCM = 9 × 45.

If the LCM of 45 and 9 is 45, Find its GCF.

LCM(45, 9) × GCF(45, 9) = 45 × 9
Since the LCM of 45 and 9 = 45
⇒ 45 × GCF(45, 9) = 405
Therefore, the greatest common factor (GCF) = 405/45 = 9.