LCM of 3, 6 and 7 - How to Find LCM of 3, 6, 7? (2024)

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

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

What is the LCM of 3, 6, and 7?

Answer: LCM of 3, 6, and 7 is 42.

LCM of 3, 6 and 7 - How to Find LCM of 3, 6, 7? (1)

Explanation:

The LCM of three non-zero integers, a(3), b(6), and c(7), is the smallest positive integer m(42) that is divisible by a(3), b(6), and c(7) without any remainder.

Methods to Find LCM of 3, 6, and 7

Let's look at the different methods for finding the LCM of 3, 6, and 7.

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

LCM of 3, 6, and 7 by Listing Multiples

LCM of 3, 6 and 7 - How to Find LCM of 3, 6, 7? (2)

To calculate the LCM of 3, 6, 7 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 3 (3, 6, 9, 12, 15 . . .), 6 (6, 12, 18, 24, 30 . . .), and 7 (7, 14, 21, 28, 35 . . .).
  • Step 2: The common multiples from the multiples of 3, 6, and 7 are 42, 84, . . .
  • Step 3: The smallest common multiple of 3, 6, and 7 is 42.

∴ The least common multiple of 3, 6, and 7 = 42.

LCM of 3, 6, and 7 by Prime Factorization

Prime factorization of 3, 6, and 7 is (3) = 31, (2 × 3) = 21 × 31, and (7) = 71 respectively. LCM of 3, 6, and 7 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 31 × 71 = 42.
Hence, the LCM of 3, 6, and 7 by prime factorization is 42.

LCM of 3, 6, and 7 by Division Method

LCM of 3, 6 and 7 - How to Find LCM of 3, 6, 7? (3)

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

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

The LCM of 3, 6, and 7 is the product of all prime numbers on the left, i.e. LCM(3, 6, 7) by division method = 2 × 3 × 7 = 42.

☛ Also Check:

  • LCM of 32 and 36 - 288
  • LCM of 72 and 96 - 288
  • LCM of 5, 6 and 8 - 120
  • LCM of 42 and 56 - 168
  • LCM of 45 and 120 - 360
  • LCM of 16, 20 and 24 - 240
  • LCM of 6 and 12 - 12

FAQs on LCM of 3, 6, and 7

What is the LCM of 3, 6, and 7?

The LCM of 3, 6, and 7 is 42. To find the LCM (least common multiple) of 3, 6, and 7, we need to find the multiples of 3, 6, and 7 (multiples of 3 = 3, 6, 9, 12 . . . . 42 . . . . ; multiples of 6 = 6, 12, 18, 24, 36, 42 . . . .; multiples of 7 = 7, 14, 21, 28, 42 . . . .) and choose the smallest multiple that is exactly divisible by 3, 6, and 7, i.e., 42.

What are the Methods to Find LCM of 3, 6, 7?

The commonly used methods to find the LCM of 3, 6, 7 are:

  • Listing Multiples
  • Prime Factorization Method
  • Division Method

What is the Relation Between GCF and LCM of 3, 6, 7?

The following equation can be used to express the relation between GCF and LCM of 3, 6, 7, i.e. LCM(3, 6, 7) = [(3 × 6 × 7) × GCF(3, 6, 7)]/[GCF(3, 6) × GCF(6, 7) × GCF(3, 7)].

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

The least number divisible by 3, 6, and 7 = LCM(3, 6, 7)
LCM of 3, 6, and 7 = 2 × 3 × 7 [Incomplete pair(s): 2, 3, 7]
⇒ Least perfect square divisible by each 3, 6, and 7 = LCM(3, 6, 7) × 2 × 3 × 7 = 1764 [Square root of 1764 = √1764 = ±42]
Therefore, 1764 is the required number.

LCM of 3, 6 and 7 - How to Find LCM of 3, 6, 7? (2024)

FAQs

LCM of 3, 6 and 7 - How to Find LCM of 3, 6, 7? ›

The LCM of 3, 6, and 7 is the product of all prime numbers on the left, i.e. LCM(3, 6, 7) by division method = 2 × 3 × 7 = 42.

How to calculate LCM? ›

LCM By Division Method
  1. First, write the numbers, separated by commas.
  2. Now divide the numbers, by the smallest prime number.
  3. If any number is not divisible, then write down that number and proceed further.
  4. Keep on dividing the row of numbers by prime numbers, unless we get the results as 1 in the complete row.
Nov 11, 2019

How do you find the LCM of two numbers? ›

Therefore, the formula to find LCM of two numbers is, LCM of two numbers = product of two numbers ÷ HCF of two numbers. Note: The LCM of two co-prime numbers is equal to the product of co-prime numbers because the highest common factor of prime numbers is 1.

What is the LCM of 3 and 7 the LCM of 3 and 7 is? ›

LCM of 3 and 7 is 21. The technique to find the smallest common multiple between any two or more numbers is known as Least Common Multiple.

What is the LCM method example? ›

The full form of LCM in Maths is Least Common Multiple.

For example, let us take two positive integers 4 and 6. Multiples of 4 are: 4,8,12,16,20,24… Multiples of 6 are: 6,12,18,24…. The common multiples for 4 and 6 are 12,24,36,48…and so on.

What is the trick to find LCM? ›

To find the LCM, you can use the prime factorization method or list the multiples of each number. Prime factorization involves breaking down numbers into their prime factors and constructing the smallest number with all the factors. Listing multiples involves finding the smallest shared multiple.

How do you find the LCM of two sets? ›

LCM by Listing Method

To calculate the LCM of the two numbers A and B by the listing method, we use the steps given below: Step 1: List the first few multiples of A and B. Step 2: Mark the common multiples from the multiples of both numbers. Step 3: Select the smallest common multiple.

Can you multiply two numbers to find the LCM? ›

Multiply the two numbers.

Divide the product by the greatest common divisor. This will give you the least common multiple of the two numbers. . So, 630 is the least common multiple of 210 and 45.

How is LCM calculated? ›

Step 1: Finding each number's prime factorization is the first step in computing the LCM using the prime factors approach. Step 2: When you write each number as a product of primes. Step 3: Now take the highest power of each prime number. Step 4: To obtain the LCM, multiply the prime numbers.

What is the fastest way to find the LCM of 3 numbers? ›

To find the LCM, you can list the multiples of each number and find the smallest one they share, or use prime factorization to break down the numbers into their prime factors and multiply the highest powers of each factor.

What is the LCM of 3 and 6 and 7? ›

LCM of 3, 6 and 7 is 42. For the given set of numbers 3, 6 and 7 the smallest common multiple for all these numbers is 42, and hence it is the LCM. 84, 126, 168 are also the common multiples.

How do you find the LCM of each set of numbers? ›

Step 1: Find the prime factors of the given numbers by repeated division method. Step 2: Write the numbers in their exponent form. Find the product of only those prime factors that have the highest power. Step 3: The product of these factors with the highest powers is the LCM of the given numbers.

What number is a multiple of 3, 6 and 7? ›

The LCM of 3, 6, and 7 is 42.

42 . . . . ; multiples of 6 = 6, 12, 18, 24, 36, 42 . . . .; multiples of 7 = 7, 14, 21, 28, 42 . . . .) and choose the smallest multiple that is exactly divisible by 3, 6, and 7, i.e., 42.

What is the LCM of 3 and 6 is 6? ›

LCM is the smallest number exactly divisible by 3 and 6. Multiples of 3 = 3, 6, 9, 12, 15, …. Multiples of 6 = 6, 12, 18, 24, 30, ….. Hence, the LCM of 3 and 6 is 6.

How do you find the LCM using the division method? ›

LCM by Division Method

In this method, divide the given numbers by common prime number until the remainder is a prime number or one. LCM will be the product obtained by multiplying all divisors and remaining prime numbers.

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