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.

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1.LCM of 6 and 15
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM of 6 and 15 is 30.

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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 MethodBy Prime Factorization MethodBy Listing Multiples

LCM of 6 and 15 by Division Method

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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 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

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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.

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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 ⇒ Least perfect square divisible by each 6 and 15 = LCM(6, 15) × 2 × 3 × 5 = 900 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 MethodListing MultiplesPrime Factorization Method

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

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

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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.