3 4 5 6 7

LCM of 2, 3, 4, 5, 6, and 7

LCM of 2, 3, 4, 5, 6, and 7 is the smallest number among all common multiples of 2, 3, 4, 5, 6, and 7. The first few multiples of 2, 3, 4, 5, 6, and 7 are (2, 4, 6, 8, 10 . . .), (3, 6, 9, 12, 15 . . .), (4, 8, 12, 16, 20 . . .), (5, 10, 15, 20, 25 . . .), (6, 12, 18, 24, 30 . . .), and (7, 14, 21, 28, 35 . . .) respectively. There are 3 commonly used methods to find LCM of 2, 3, 4, 5, 6, and 7 – by division method, by prime factorization, and by listing multiples.

1.	LCM of 2, 3, 4, 5, 6, and 7
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 2, 3, 4, 5, 6, and 7?

Answer:
LCM of 2, 3, 4, 5, 6, and 7 is 420.

Explanation:

The LCM of six non-zero integers, a(2), b(3), c(4), d(5), e(6), and f(7), is the smallest positive integer m(420) that is divisible by a(2), b(3), c(4), d(5), e(6), and f(7) without any remainder.

Methods to Find LCM of 2, 3, 4, 5, 6, and 7

Let’s look at the different methods for finding the LCM of 2, 3, 4, 5, 6, and 7.

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

LCM of 2, 3, 4, 5, 6, and 7 by Prime Factorization

Prime factorization of 2, 3, 4, 5, 6, and 7 is (2) = 2¹, (3) = 3¹, (2 × 2) = 2², (5) = 5¹, (2 × 3) = 2¹
× 3¹, and (7) = 7¹
respectively. LCM of 2, 3, 4, 5, 6, and 7 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2²
× 3¹
× 5¹
× 7¹
= 420.
Hence, the LCM of 2, 3, 4, 5, 6, and 7 by prime factorization is 420.

LCM of 2, 3, 4, 5, 6, and 7 by Listing Multiples

To calculate the LCM of 2, 3, 4, 5, 6, and 7 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, . . .420, . . .), 3 (3, 6, 9, 12, 15, . . .420, . . .), 4 (4, 8, 12, 16, 20, . . .420, . . .), 5 (5, 10, 15, 20, 25, . . .420, . . .), 6 (6, 12, 18, 24, 30, . . .420, . . .), and 7 (7, 14, 21, 28, 35, . . .420, . . .).
• Step 2:
  The common multiples from the multiples of 2, 3, 4, 5, 6, and 7 are 420, 840, . . .
• Step 3:
  The smallest common multiple of 2, 3, 4, 5, 6, and 7 is 420.

∴ The least common multiple of 2, 3, 4, 5, 6, and 7 = 420.

LCM of 2, 3, 4, 5, 6, and 7 by Division Method

To calculate the LCM of 2, 3, 4, 5, 6, and 7 by the division method, we will divide the numbers(2, 3, 4, 5, 6, 7) by their prime factors (preferably common). The product of these divisors gives the LCM of 2, 3, 4, 5, 6, and 7.

• Step 1:
  Find the smallest prime number that is a factor of at least one of the numbers, 2, 3, 4, 5, 6, and 7. Write this prime number(2) on the left of the given numbers(2, 3, 4, 5, 6, and 7), separated as saban the ladder arrangement.
• Step 2:
  If any of the given numbers (2, 3, 4, 5, 6, 7) 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 mencicil only 1s are left in the last row.

The LCM of 2, 3, 4, 5, 6, and 7 is the product of all prime numbers on the left, i.e. LCM(2, 3, 4, 5, 6, 7) by division method = 2 × 2 × 3 × 5 × 7 = 420.

☛ Also Check:

• LCM of 4, 12 and 16 – 48
• LCM of 6 and 18 – 18
• LCM of 12 and 60 – 60
• LCM of 12, 18 and 20 – 180
• LCM of 5, 6 and 7 – 210
• LCM of 80 and 120 – 240
• LCM of 20 and 50 – 100

FAQs on LCM of 2, 3, 4, 5, 6, and 7

What is the LCM of 2, 3, 4, 5, 6, and 7?

The

LCM of 2, 3, 4, 5, 6, and 7 is 420
. To find the LCM of 2, 3, 4, 5, 6, and 7, we need to find the multiples of 2, 3, 4, 5, 6, and 7 (multiples of 2 = 2, 4, 6, 8, . . . 420, . . .; multiples of 3 = 3, 6, 9, 12,. . . 420, . . .; multiples of 4 = 4, 8, 12, 16, . . .420, . . .; multiples of 5 = 5, 10, 15, 20, . . . 420, . . .; multiples of 6 = 6, 12, 18, 24, . . . 420, . . .; multiples of 7 = 7, 14, 21, 28,. . . 420, . . .) and choose the smallest multiple that is exactly divisible by 2, 3, 4, 5, 6, and 7, i.e., 420.

What is the Least Perfect Square Divisible by 2, 3, 4, 5, 6, and 7?

The least number divisible by 2, 3, 4, 5, 6, and 7 = LCM(2, 3, 4, 5, 6, 7)
LCM of 2, 3, 4, 5, 6, and 7 =
2 × 2
× 3 × 5 × 7 [Incomplete pair(s): 3, 5, 7]
⇒ Least perfect square divisible by each 2, 3, 4, 5, 6, and 7 = LCM(2, 3, 4, 5, 6, 7) × 3 × 5 × 7 = 44100 [Square root of 44100 = √44100 = ±210]
Therefore, 44100 is the required number.

What are the Methods to Find LCM of 2, 3, 4, 5, 6, and 7?

The commonly used methods to find the
LCM of 2, 3, 4, 5, 6, and 7
are:

• Division Method
• Prime Factorization Method
• Listing Multiples

Which of the following is the LCM of 2, 3, 4, 5, 6, and 7? 96, 42, 32, 420

The value of LCM of 2, 3, 4, 5, 6, 7 is the smallest common multiple of 2, 3, 4, 5, 6, and 7. The number satisfying the given condition is 420.