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LCM of 2, 4, 6, 8, 10, and 12

LCM of 2, 4, 6, 8, 10, and 12 is the smallest number among all common multiples of 2, 4, 6, 8, 10, and 12. The first few multiples of 2, 4, 6, 8, 10, and 12 are (2, 4, 6, 8, 10 . . .), (4, 8, 12, 16, 20 . . .), (6, 12, 18, 24, 30 . . .), (8, 16, 24, 32, 40 . . .), (10, 20, 30, 40, 50 . . .), and (12, 24, 36, 48, 60 . . .) respectively. There are 3 commonly used methods to find LCM of 2, 4, 6, 8, 10, and 12 - by prime factorization, by listing multiples, and by division method.

1. LCM of 2, 4, 6, 8, 10, and 12
2. List of Methods
3. Solved Examples
4. FAQs

What is the LCM of 2, 4, 6, 8, 10, and 12?

Answer: LCM of 2, 4, 6, 8, 10, and 12 is 120.

LCM of 2, 4, 6, 8, 10, and 12

Explanation:

The LCM of six non-zero integers, a(2), b(4), c(6), d(8), e(10), and f(12), is the smallest positive integer m(120) that is divisible by a(2), b(4), c(6), d(8), e(10), and f(12) without any remainder.

Methods to Find LCM of 2, 4, 6, 8, 10, and 12

The methods to find the LCM of 2, 4, 6, 8, 10, and 12 are explained below.

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

LCM of 2, 4, 6, 8, 10, and 12 by Prime Factorization

Prime factorization of 2, 4, 6, 8, 10, and 12 is (2) = 21, (2 × 2) = 22, (2 × 3) = 21 × 31, (2 × 2 × 2) = 23, (2 × 5) = 21 × 51, and (2 × 2 × 3) = 22 × 31 respectively. LCM of 2, 4, 6, 8, 10, and 12 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 31 × 51 = 120.
Hence, the LCM of 2, 4, 6, 8, 10, and 12 by prime factorization is 120.

LCM of 2, 4, 6, 8, 10, and 12 by Listing Multiples

To calculate the LCM of 2, 4, 6, 8, 10, and 12 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 2 (2, 4, 6, 8, 10, . . ., 120, . . .), 4 (4, 8, 12, 16, 20, . . .120, . . .), 6 (6, 12, 18, 24, 30, . . .120, . . .), 8 (8, 16, 24, 32, 40, . . .120, . . .), 10 (10, 20, 30, 40, 50, . . .120, . . .), and 12 (12, 24, 36, 48, 60, . . .120, . . .).
  • Step 2: The common multiples from the multiples of 2, 4, 6, 8, 10, and 12 are 120, 240, . . .
  • Step 3: The smallest common multiple of 2, 4, 6, 8, 10, and 12 is 120.

∴ The least common multiple of 2, 4, 6, 8, 10, and 12 = 120.

LCM of 2, 4, 6, 8, 10, and 12 by Division Method

LCM of 2, 4, 6, 8, 10, and 12 by Division Method

To calculate the LCM of 2, 4, 6, 8, 10, and 12 by the division method, we will divide the numbers(2, 4, 6, 8, 10, 12) by their prime factors (preferably common). The product of these divisors gives the LCM of 2, 4, 6, 8, 10, and 12.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2, 4, 6, 8, 10, and 12. Write this prime number(2) on the left of the given numbers(2, 4, 6, 8, 10, and 12), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (2, 4, 6, 8, 10, 12) 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 2, 4, 6, 8, 10, and 12 is the product of all prime numbers on the left, i.e. LCM(2, 4, 6, 8, 10, 12) by division method = 2 × 2 × 2 × 3 × 5 = 120.

☛ Also Check:

LCM of 2, 4, 6, 8, 10, and 12 Examples

  1. Example 1: Which of the following is the LCM of 2, 4, 6, 8, 10, 12? 96, 120, 40, 110.

    Solution:

    The value of LCM of 2, 4, 6, 8, 10, and 12 is the smallest common multiple of 2, 4, 6, 8, 10, and 12.

    The number satisfying the given condition is 120.

    ∴LCM(2, 4, 6, 8, 10, 12) = 120.

  2. Example 2: Find the smallest number which when divided by 2, 4, 6, 8, 10, and 12 leaves 1 as the remainder in each case.

    Solution:

    The smallest number exactly divisible by 2, 4, 6, 8, 10, and 12 = LCM(2, 4, 6, 8, 10, 12)

    ⇒ Smallest number which leaves 1 as remainder when divided by 2, 4, 6, 8, 10, and 12 = LCM(2, 4, 6, 8, 10, 12) + 1

    • 2 = 21
    • 4 = 22
    • 6 = 21 × 31
    • 8 = 23
    • 10 = 21 × 51
    • 12 = 22 × 31

    LCM(2, 4, 6, 8, 10, 12) = 23 × 31 × 51 = 120

    ⇒ The required number = 120 + 1 = 121.

  3. Example 3: Find the smallest number that is divisible by 2, 4, 6, 8, 10, and 12 exactly.

    Solution:

    The value of LCM(2, 4, 6, 8, 10, 12) will be the smallest number that is exactly divisible by 2, 4, 6, 8, 10, and 12.
    ⇒ Multiples of 2, 4, 6, 8, 10, and 12:

    • Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, . . ., 114, 116, 118, 120, . . .
    • Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . ., 112, 116, 120, . . .
    • Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . ., 102, 108, 114, 120, . . .
    • Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, . . ., 104, 112, 120, . . .
    • Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, . . .
    • Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . .

    Therefore, the LCM of 2, 4, 6, 8, 10, and 12 is 120.

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FAQs on LCM of 2, 4, 6, 8, 10, and 12

What is the LCM of 2, 4, 6, 8, 10, and 12?

The LCM of 2, 4, 6, 8, 10, and 12 is 120. To find the LCM of 2, 4, 6, 8, 10, and 12, we need to find the multiples of 2, 4, 6, 8, 10, and 12 (multiples of 2 = 2, 4, 6, 8, . . .120, . . .; multiples of 4 = 4, 8, 12, 16, . . .120, . . .; multiples of 6 = 6, 12, 18, 24, . . . 120, . . .; multiples of 8 = 8, 16, 24, 32, . . . 120, . . ; multiples of 10 = 10, 20, 30, 40,. . . 120, . . .; multiples of 12 = 12, 24, 36, 48 . . . 120, . . .) and choose the smallest multiple that is exactly divisible by 2, 4, 6, 8, 10, and 12, i.e., 120.

Which of the following is the LCM of 2, 4, 6, 8, 10, and 12? 35, 120, 21, 52

The value of LCM of 2, 4, 6, 8, 10, 12 is the smallest common multiple of 2, 4, 6, 8, 10, and 12. The number satisfying the given condition is 120.

What are the Methods to Find LCM of 2, 4, 6, 8, 10, and 12?

The commonly used methods to find the LCM of 2, 4, 6, 8, 10, and 12 are:

  • Prime Factorization Method
  • Division Method
  • Listing Multiples

What is the Least Perfect Square Divisible by 2, 4, 6, 8, 10, and 12?

The least number divisible by 2, 4, 6, 8, 10, and 12 = LCM(2, 4, 6, 8, 10, 12)
LCM of 2, 4, 6, 8, 10, and 12 = 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 2, 4, 6, 8, 10, and 12 = LCM(2, 4, 6, 8, 10, 12) × 2 × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

 
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