LCM of 6 and 15

LCM of 6 and 15 is the smallest number among all common multiples of 6 and 15. The first few multiples of 6 and 15 are (6, 12, 18, 24, 30, 36, . . . ) and (15, 30, 45, 60, 75, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 15 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 6 and 15 is 30.

Explanation:

The LCM of two non-zero integers, x(6) and y(15), is the smallest positive integer m(30) that is divisible by both x(6) and y(15) without any remainder.

The methods to find the LCM of 6 and 15 are explained below.

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

LCM of 6 and 15 by Division Method

To calculate the LCM of 6 and 15 by the division method, we will divide the numbers(6, 15) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 15.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 15. Write this prime number(2) on the left of the given numbers(6 and 15), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 15) 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 15 is the product of all prime numbers on the left, i.e. LCM(6, 15) by division method = 2 × 3 × 5 = 30.

LCM of 6 and 15 by Prime Factorization

Prime factorization of 6 and 15 is (2 × 3) = 2¹ × 3¹ and (3 × 5) = 3¹ × 5¹ respectively. LCM of 6 and 15 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 15 by prime factorization is 30.

LCM of 6 and 15 by Listing Multiples

To calculate the LCM of 6 and 15 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 15 (15, 30, 45, 60, 75, . . . . )
• Step 2: The common multiples from the multiples of 6 and 15 are 30, 60, . . .
• Step 3: The smallest common multiple of 6 and 15 is 30.

∴ The least common multiple of 6 and 15 = 30.

☛ Also Check:

• LCM of 8, 10 and 15 - 120
• LCM of 6 and 8 - 24
• LCM of 10 and 25 - 50
• LCM of 30 and 90 - 90
• LCM of 15, 25, 40 and 75 - 600
• LCM of 48 and 60 - 240
• LCM of 6, 9 and 12 - 36

FAQs on LCM of 6 and 15

What is the LCM of 6 and 15?

The LCM of 6 and 15 is 30. To find the least common multiple (LCM) of 6 and 15, we need to find the multiples of 6 and 15 (multiples of 6 = 6, 12, 18, 24 . . . . 30; multiples of 15 = 15, 30, 45, 60) and choose the smallest multiple that is exactly divisible by 6 and 15, i.e., 30.

What is the Least Perfect Square Divisible by 6 and 15?

The least number divisible by 6 and 15 = LCM(6, 15)
LCM of 6 and 15 = 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 6 and 15 = LCM(6, 15) × 2 × 3 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

What are the Methods to Find LCM of 6 and 15?

The commonly used methods to find the LCM of 6 and 15 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

If the LCM of 15 and 6 is 30, Find its GCF.

LCM(15, 6) × GCF(15, 6) = 15 × 6
Since the LCM of 15 and 6 = 30
⇒ 30 × GCF(15, 6) = 90
Therefore, the greatest common factor (GCF) = 90/30 = 3.

Which of the following is the LCM of 6 and 15? 30, 24, 36, 11

The value of LCM of 6, 15 is the smallest common multiple of 6 and 15. The number satisfying the given condition is 30.