LCM of 9 and 15

LCM of 9 and 15 is the smallest number among all common multiples of 9 and 15. The first few multiples of 9 and 15 are (9, 18, 27, 36, 45, . . . ) and (15, 30, 45, 60, 75, 90, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 15 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 9 and 15 is 45.

Explanation:

The LCM of two non-zero integers, x(9) and y(15), is the smallest positive integer m(45) that is divisible by both x(9) and y(15) without any remainder.

Let's look at the different methods for finding the LCM of 9 and 15.

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

LCM of 9 and 15 by Division Method

To calculate the LCM of 9 and 15 by the division method, we will divide the numbers(9, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 15.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 15. Write this prime number(3) on the left of the given numbers(9 and 15), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (9, 15) 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 15 is the product of all prime numbers on the left, i.e. LCM(9, 15) by division method = 3 × 3 × 5 = 45.

LCM of 9 and 15 by Prime Factorization

Prime factorization of 9 and 15 is (3 × 3) = 3² and (3 × 5) = 3¹ × 5¹ respectively. LCM of 9 and 15 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3² × 5¹ = 45.
Hence, the LCM of 9 and 15 by prime factorization is 45.

LCM of 9 and 15 by Listing Multiples

To calculate the LCM of 9 and 15 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, . . . ) and 15 (15, 30, 45, 60, 75, 90, . . . . )
• Step 2: The common multiples from the multiples of 9 and 15 are 45, 90, . . .
• Step 3: The smallest common multiple of 9 and 15 is 45.

∴ The least common multiple of 9 and 15 = 45.

☛ Also Check:

• LCM of 36 and 84 - 252
• LCM of 36 and 63 - 252
• LCM of 24 and 54 - 216
• LCM of 2601 and 2616 - 2268072
• LCM of 17 and 34 - 34
• LCM of 7, 8, 14 and 21 - 168
• LCM of 8, 15 and 20 - 120

FAQs on LCM of 9 and 15

What is the LCM of 9 and 15?

The LCM of 9 and 15 is 45. To find the LCM of 9 and 15, we need to find the multiples of 9 and 15 (multiples of 9 = 9, 18, 27, 36 . . . . 45; multiples of 15 = 15, 30, 45, 60) and choose the smallest multiple that is exactly divisible by 9 and 15, i.e., 45.

What is the Relation Between GCF and LCM of 9, 15?

The following equation can be used to express the relation between GCF and LCM of 9 and 15, i.e. GCF × LCM = 9 × 15.

Which of the following is the LCM of 9 and 15? 21, 45, 18, 30

The value of LCM of 9, 15 is the smallest common multiple of 9 and 15. The number satisfying the given condition is 45.

If the LCM of 15 and 9 is 45, Find its GCF.

LCM(15, 9) × GCF(15, 9) = 15 × 9
Since the LCM of 15 and 9 = 45
⇒ 45 × GCF(15, 9) = 135
Therefore, the GCF = 135/45 = 3.

What is the Least Perfect Square Divisible by 9 and 15?

The least number divisible by 9 and 15 = LCM(9, 15)
LCM of 9 and 15 = 3 × 3 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 9 and 15 = LCM(9, 15) × 5 = 225 [Square root of 225 = √225 = ±15]
Therefore, 225 is the required number.