What is the least common multiple of 2 and 7

What is the Least Common Multiple (LCM) of 2, 7, and 11? Here we will show you step-by-step how to find the Least Common Multiple of 2, 7, and 11.

Step 1) First we find and list the prime factors of 2, 7, and 11 (Prime Factorization):

Prime Factors of 2:
2

Prime Factors of 7:
7

Prime Factors of 11:
11

2, 7, 11 Step 3) Finally, we multiply the prime numbers from Step 2 together.

2 x 7 x 11 = 154 That's it. The Least Common Multiple (LCM) of 2, 7, and 11 is 154.

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Least Common Multiple (LCM) of 2, 7, and 12
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Multiples of #2# are #{2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,...}#

Multiples of #3# are #{3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,..}#

Multiples of #7# are #{7,14,21,28,35,42,49,56,...}#

Common multiples are #{42,...}#

Least Common Multiple is #42#.

The least common multiple (also called the lowest common multiple or smallest common multiple or LCM) of one or more integer numbers is the smallest positive integer divisible by all these numbers.

One way to find the least common multiple of two numbers is first to list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor by the greatest number of times it occurs.

For three or more numbers, proceed similarly, multiple the largest found powers of prime factors of given numbers.

What is the Least Common Multiple of 2 and 7?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 2 and 7 is 14.

LCM(2,7) = 14

Least Common Multiple of 2 and 7 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2 and 7, than apply into the LCM equation.

GCF(2,7) = 1
LCM(2,7) = ( 2 × 7) / 1
LCM(2,7) = 14 / 1
LCM(2,7) = 14

Least common multiple can be found by multiplying the highest exponent prime factors of 2 and 7. First we will calculate the prime factors of 2 and 7.

Prime Factorization of 2

Prime factors of 2 are 2. Prime factorization of 2 in exponential form is:

2 = 21

Prime Factorization of 7

Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:

7 = 71

Now multiplying the highest exponent prime factors to calculate the LCM of 2 and 7.

LCM(2,7) = 21 × 71
LCM(2,7) = 14

What is the LCM of 2 and 7?

The LCM of 2 and 7 is 14.

Steps to find LCM

1. Find the prime factorization of 2
   2 = 2
2. Find the prime factorization of 7
   7 = 7
3. Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

   LCM = 2 × 7

4. LCM = 14

MathStep (Works offline)

Find least common multiple (LCM) of: 4 & 14 6 & 21 10 & 35 14 & 49 4 & 7 2 & 14 6 & 7 2 & 21 10 & 7 2 & 35 14 & 7 2 & 49

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Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here.

LCM of 2 and 7 is the smallest number among all common multiples of 2 and 7. The first few multiples of 2 and 7 are (2, 4, 6, 8, 10, 12, 14, . . . ) and (7, 14, 21, 28, 35, 42, 49, . . . ) respectively. There are 3 commonly used methods to find LCM of 2 and 7 - by division method, by prime factorization, and by listing multiples.

What is the LCM of 2 and 7?

Answer: LCM of 2 and 7 is 14.

Explanation:

The LCM of two non-zero integers, x(2) and y(7), is the smallest positive integer m(14) that is divisible by both x(2) and y(7) without any remainder.

Methods to Find LCM of 2 and 7

Let's look at the different methods for finding the LCM of 2 and 7.

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

LCM of 2 and 7 by Listing Multiples

To calculate the LCM of 2 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, 12, 14, . . . ) and 7 (7, 14, 21, 28, 35, 42, 49, . . . . )
• Step 2: The common multiples from the multiples of 2 and 7 are 14, 28, . . .
• Step 3: The smallest common multiple of 2 and 7 is 14.

∴ The least common multiple of 2 and 7 = 14.

LCM of 2 and 7 by Prime Factorization

Prime factorization of 2 and 7 is (2) = 21 and (7) = 71 respectively. LCM of 2 and 7 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 71 = 14.
Hence, the LCM of 2 and 7 by prime factorization is 14.

LCM of 2 and 7 by Division Method

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

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2 and 7. Write this prime number(2) on the left of the given numbers(2 and 7), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (2, 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 2 and 7 is the product of all prime numbers on the left, i.e. LCM(2, 7) by division method = 2 × 7 = 14.

☛ Also Check:

• LCM of 12 and 40 - 120
• LCM of 6, 9 and 15 - 90
• LCM of 2 and 13 - 26
• LCM of 63 and 81 - 567
• LCM of 14 and 24 - 168
• LCM of 15 and 40 - 120
• LCM of 6, 8 and 15 - 120

FAQs on LCM of 2 and 7

What is the LCM of 2 and 7?

The LCM of 2 and 7 is 14. To find the least common multiple of 2 and 7, we need to find the multiples of 2 and 7 (multiples of 2 = 2, 4, 6, 8 . . . . 14; multiples of 7 = 7, 14, 21, 28) and choose the smallest multiple that is exactly divisible by 2 and 7, i.e., 14.

How to Find the LCM of 2 and 7 by Prime Factorization?

To find the LCM of 2 and 7 using prime factorization, we will find the prime factors, (2 = 2) and (7 = 7). LCM of 2 and 7 is the product of prime factors raised to their respective highest exponent among the numbers 2 and 7.
⇒ LCM of 2, 7 = 21 × 71 = 14.

What are the Methods to Find LCM of 2 and 7?

The commonly used methods to find the LCM of 2 and 7 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

Which of the following is the LCM of 2 and 7? 45, 18, 14, 5

The value of LCM of 2, 7 is the smallest common multiple of 2 and 7. The number satisfying the given condition is 14.

If the LCM of 7 and 2 is 14, Find its GCF.

LCM(7, 2) × GCF(7, 2) = 7 × 2
Since the LCM of 7 and 2 = 14
⇒ 14 × GCF(7, 2) = 14
Therefore, the GCF (greatest common factor) = 14/14 = 1.

Which are the common factor of both 2 and 7?

What is the LCM of 2 and 1 7?