LCM of 6 and 14

LCM of 6 and 14 is the smallest number among all common multiples of 6 and 14. The first few multiples of 6 and 14 are (6, 12, 18, 24, 30, . . . ) and (14, 28, 42, 56, 70, 84, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 14 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 6 and 14 is 42.

Explanation:

The LCM of two non-zero integers, x(6) and y(14), is the smallest positive integer m(42) that is divisible by both x(6) and y(14) without any remainder.

The methods to find the LCM of 6 and 14 are explained below.

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

LCM of 6 and 14 by Division Method

To calculate the LCM of 6 and 14 by the division method, we will divide the numbers(6, 14) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 14.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 14. Write this prime number(2) on the left of the given numbers(6 and 14), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 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 6 and 14 is the product of all prime numbers on the left, i.e. LCM(6, 14) by division method = 2 × 3 × 7 = 42.

LCM of 6 and 14 by Prime Factorization

Prime factorization of 6 and 14 is (2 × 3) = 2¹ × 3¹ and (2 × 7) = 2¹ × 7¹ respectively. LCM of 6 and 14 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 7¹ = 42.
Hence, the LCM of 6 and 14 by prime factorization is 42.

LCM of 6 and 14 by Listing Multiples

To calculate the LCM of 6 and 14 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, . . . ) and 14 (14, 28, 42, 56, 70, 84, . . . . )
• Step 2: The common multiples from the multiples of 6 and 14 are 42, 84, . . .
• Step 3: The smallest common multiple of 6 and 14 is 42.

∴ The least common multiple of 6 and 14 = 42.

☛ Also Check:

• LCM of 9 and 18 - 18
• LCM of 2 and 3 - 6
• LCM of 378, 180 and 420 - 3780
• LCM of 6, 9 and 15 - 90
• LCM of 2, 3 and 4 - 12
• LCM of 2601 and 2616 - 2268072
• LCM of 4 and 8 - 8

FAQs on LCM of 6 and 14

What is the LCM of 6 and 14?

The LCM of 6 and 14 is 42. To find the LCM of 6 and 14, we need to find the multiples of 6 and 14 (multiples of 6 = 6, 12, 18, 24 . . . . 42; multiples of 14 = 14, 28, 42, 56) and choose the smallest multiple that is exactly divisible by 6 and 14, i.e., 42.

If the LCM of 14 and 6 is 42, Find its GCF.

LCM(14, 6) × GCF(14, 6) = 14 × 6
Since the LCM of 14 and 6 = 42
⇒ 42 × GCF(14, 6) = 84
Therefore, the greatest common factor = 84/42 = 2.

What is the Least Perfect Square Divisible by 6 and 14?

The least number divisible by 6 and 14 = LCM(6, 14)
LCM of 6 and 14 = 2 × 3 × 7 [Incomplete pair(s): 2, 3, 7]
⇒ Least perfect square divisible by each 6 and 14 = LCM(6, 14) × 2 × 3 × 7 = 1764 [Square root of 1764 = √1764 = ±42]
Therefore, 1764 is the required number.

How to Find the LCM of 6 and 14 by Prime Factorization?

To find the LCM of 6 and 14 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (14 = 2 × 7). LCM of 6 and 14 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 14.
⇒ LCM of 6, 14 = 2¹ × 3¹ × 7¹ = 42.

What are the Methods to Find LCM of 6 and 14?

The commonly used methods to find the LCM of 6 and 14 are:

• Listing Multiples
• Prime Factorization Method
• Division Method