LCM of 6 and 30

LCM of 6 and 30 is the smallest number among all common multiples of 6 and 30. The first few multiples of 6 and 30 are (6, 12, 18, 24, 30, 36, . . . ) and (30, 60, 90, 120, 150, 180, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 30 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 6 and 30 is 30.

Explanation:

The LCM of two non-zero integers, x(6) and y(30), is the smallest positive integer m(30) that is divisible by both x(6) and y(30) without any remainder.

Let's look at the different methods for finding the LCM of 6 and 30.

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

LCM of 6 and 30 by Division Method

To calculate the LCM of 6 and 30 by the division method, we will divide the numbers(6, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 30.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 30. Write this prime number(2) on the left of the given numbers(6 and 30), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 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 6 and 30 is the product of all prime numbers on the left, i.e. LCM(6, 30) by division method = 2 × 3 × 5 = 30.

LCM of 6 and 30 by Listing Multiples

To calculate the LCM of 6 and 30 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, 36, . . . ) and 30 (30, 60, 90, 120, 150, 180, . . . . )
• Step 2: The common multiples from the multiples of 6 and 30 are 30, 60, . . .
• Step 3: The smallest common multiple of 6 and 30 is 30.

∴ The least common multiple of 6 and 30 = 30.

LCM of 6 and 30 by Prime Factorization

Prime factorization of 6 and 30 is (2 × 3) = 2¹ × 3¹ and (2 × 3 × 5) = 2¹ × 3¹ × 5¹ respectively. LCM of 6 and 30 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 5¹ = 30.
Hence, the LCM of 6 and 30 by prime factorization is 30.

☛ Also Check:

• LCM of 18, 24 and 30 - 360
• LCM of 20 and 30 - 60
• LCM of 2, 5 and 8 - 40
• LCM of 3 and 14 - 42
• LCM of 18 and 72 - 72
• LCM of 6 and 21 - 42
• LCM of 8, 9 and 12 - 72

FAQs on LCM of 6 and 30

What is the LCM of 6 and 30?

The LCM of 6 and 30 is 30. To find the least common multiple of 6 and 30, we need to find the multiples of 6 and 30 (multiples of 6 = 6, 12, 18, 24 . . . . 30; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 6 and 30, i.e., 30.

If the LCM of 30 and 6 is 30, Find its GCF.

LCM(30, 6) × GCF(30, 6) = 30 × 6
Since the LCM of 30 and 6 = 30
⇒ 30 × GCF(30, 6) = 180
Therefore, the GCF = 180/30 = 6.

What are the Methods to Find LCM of 6 and 30?

The commonly used methods to find the LCM of 6 and 30 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

What is the Least Perfect Square Divisible by 6 and 30?

The least number divisible by 6 and 30 = LCM(6, 30)
LCM of 6 and 30 = 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 6 and 30 = LCM(6, 30) × 2 × 3 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

How to Find the LCM of 6 and 30 by Prime Factorization?

To find the LCM of 6 and 30 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (30 = 2 × 3 × 5). LCM of 6 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 30.
⇒ LCM of 6, 30 = 2¹ × 3¹ × 5¹ = 30.