LCM of 7 and 14

LCM of 7 and 14 is the smallest number among all common multiples of 7 and 14. The first few multiples of 7 and 14 are (7, 14, 21, 28, 35, . . . ) and (14, 28, 42, 56, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 14 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 7 and 14 is 14.

Explanation:

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

The methods to find the LCM of 7 and 14 are explained below.

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

LCM of 7 and 14 by Division Method

To calculate the LCM of 7 and 14 by the division method, we will divide the numbers(7, 14) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 14.

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

LCM of 7 and 14 by Prime Factorization

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

LCM of 7 and 14 by Listing Multiples

To calculate the LCM of 7 and 14 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 7 (7, 14, 21, 28, 35, . . . ) and 14 (14, 28, 42, 56, . . . . )
• Step 2: The common multiples from the multiples of 7 and 14 are 14, 28, . . .
• Step 3: The smallest common multiple of 7 and 14 is 14.

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

☛ Also Check:

• LCM of 24 and 40 - 120
• LCM of 72, 126 and 168 - 504
• LCM of 20 and 25 - 100
• LCM of 12 and 30 - 60
• LCM of 9 and 21 - 63
• LCM of 16 and 22 - 176
• LCM of 2, 3, 4, 5, 6 and 7 - 420

FAQs on LCM of 7 and 14

What is the LCM of 7 and 14?

The LCM of 7 and 14 is 14. To find the least common multiple of 7 and 14, we need to find the multiples of 7 and 14 (multiples of 7 = 7, 14, 21, 28; multiples of 14 = 14, 28, 42, 56) and choose the smallest multiple that is exactly divisible by 7 and 14, i.e., 14.

What is the Relation Between GCF and LCM of 7, 14?

The following equation can be used to express the relation between GCF and LCM of 7 and 14, i.e. GCF × LCM = 7 × 14.

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

LCM(14, 7) × GCF(14, 7) = 14 × 7
Since the LCM of 14 and 7 = 14
⇒ 14 × GCF(14, 7) = 98
Therefore, the GCF (greatest common factor) = 98/14 = 7.

What are the Methods to Find LCM of 7 and 14?

The commonly used methods to find the LCM of 7 and 14 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

How to Find the LCM of 7 and 14 by Prime Factorization?

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