LCM of 9 and 30

LCM of 9 and 30 is the smallest number among all common multiples of 9 and 30. The first few multiples of 9 and 30 are (9, 18, 27, 36, . . . ) and (30, 60, 90, 120, 150, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 30 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 9 and 30 is 90.

Explanation:

The LCM of two non-zero integers, x(9) and y(30), is the smallest positive integer m(90) that is divisible by both x(9) and y(30) without any remainder.

The methods to find the LCM of 9 and 30 are explained below.

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

LCM of 9 and 30 by Division Method

To calculate the LCM of 9 and 30 by the division method, we will divide the numbers(9, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 30.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 30. Write this prime number(2) on the left of the given numbers(9 and 30), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (9, 30) is a multiple of 2, divide it by 2 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 30 is the product of all prime numbers on the left, i.e. LCM(9, 30) by division method = 2 × 3 × 3 × 5 = 90.

LCM of 9 and 30 by Listing Multiples

To calculate the LCM of 9 and 30 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, . . . ) and 30 (30, 60, 90, 120, 150, . . . . )
• Step 2: The common multiples from the multiples of 9 and 30 are 90, 180, . . .
• Step 3: The smallest common multiple of 9 and 30 is 90.

∴ The least common multiple of 9 and 30 = 90.

LCM of 9 and 30 by Prime Factorization

Prime factorization of 9 and 30 is (3 × 3) = 3² and (2 × 3 × 5) = 2¹ × 3¹ × 5¹ respectively. LCM of 9 and 30 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 5¹ = 90.
Hence, the LCM of 9 and 30 by prime factorization is 90.

☛ Also Check:

• LCM of 20 and 25 - 100
• LCM of 54 and 60 - 540
• LCM of 4 and 6 - 12
• LCM of 27 and 36 - 108
• LCM of 13 and 26 - 26
• LCM of 24 and 60 - 120
• LCM of 11 and 12 - 132

FAQs on LCM of 9 and 30

What is the LCM of 9 and 30?

The LCM of 9 and 30 is 90. To find the LCM of 9 and 30, we need to find the multiples of 9 and 30 (multiples of 9 = 9, 18, 27, 36 . . . . 90; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 9 and 30, i.e., 90.

What is the Least Perfect Square Divisible by 9 and 30?

The least number divisible by 9 and 30 = LCM(9, 30)
LCM of 9 and 30 = 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 9 and 30 = LCM(9, 30) × 2 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

How to Find the LCM of 9 and 30 by Prime Factorization?

To find the LCM of 9 and 30 using prime factorization, we will find the prime factors, (9 = 3 × 3) and (30 = 2 × 3 × 5). LCM of 9 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 9 and 30.
⇒ LCM of 9, 30 = 2¹ × 3² × 5¹ = 90.

If the LCM of 30 and 9 is 90, Find its GCF.

LCM(30, 9) × GCF(30, 9) = 30 × 9
Since the LCM of 30 and 9 = 90
⇒ 90 × GCF(30, 9) = 270
Therefore, the GCF = 270/90 = 3.

Which of the following is the LCM of 9 and 30? 28, 20, 5, 90

The value of LCM of 9, 30 is the smallest common multiple of 9 and 30. The number satisfying the given condition is 90.