LCM of 8 and 14

LCM of 8 and 14 is the smallest number among all common multiples of 8 and 14. The first few multiples of 8 and 14 are (8, 16, 24, 32, 40, 48, . . . ) and (14, 28, 42, 56, 70, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 14 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 8 and 14 is 56.

Explanation:

The LCM of two non-zero integers, x(8) and y(14), is the smallest positive integer m(56) that is divisible by both x(8) and y(14) without any remainder.

The methods to find the LCM of 8 and 14 are explained below.

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

LCM of 8 and 14 by Division Method

To calculate the LCM of 8 and 14 by the division method, we will divide the numbers(8, 14) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 14.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 14. Write this prime number(2) on the left of the given numbers(8 and 14), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 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 8 and 14 is the product of all prime numbers on the left, i.e. LCM(8, 14) by division method = 2 × 2 × 2 × 7 = 56.

LCM of 8 and 14 by Listing Multiples

To calculate the LCM of 8 and 14 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 8 (8, 16, 24, 32, 40, 48, . . . ) and 14 (14, 28, 42, 56, 70, . . . . )
• Step 2: The common multiples from the multiples of 8 and 14 are 56, 112, . . .
• Step 3: The smallest common multiple of 8 and 14 is 56.

∴ The least common multiple of 8 and 14 = 56.

LCM of 8 and 14 by Prime Factorization

Prime factorization of 8 and 14 is (2 × 2 × 2) = 2³ and (2 × 7) = 2¹ × 7¹ respectively. LCM of 8 and 14 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 7¹ = 56.
Hence, the LCM of 8 and 14 by prime factorization is 56.

☛ Also Check:

• LCM of 6 and 30 - 30
• LCM of 24 and 36 - 72
• LCM of 32 and 40 - 160
• LCM of 5 and 15 - 15
• LCM of 27 and 45 - 135
• LCM of 4, 7 and 10 - 140
• LCM of 4, 6 and 9 - 36

FAQs on LCM of 8 and 14

What is the LCM of 8 and 14?

The LCM of 8 and 14 is 56. To find the LCM (least common multiple) of 8 and 14, we need to find the multiples of 8 and 14 (multiples of 8 = 8, 16, 24, 32 . . . . 56; multiples of 14 = 14, 28, 42, 56) and choose the smallest multiple that is exactly divisible by 8 and 14, i.e., 56.

If the LCM of 14 and 8 is 56, Find its GCF.

LCM(14, 8) × GCF(14, 8) = 14 × 8
Since the LCM of 14 and 8 = 56
⇒ 56 × GCF(14, 8) = 112
Therefore, the greatest common factor = 112/56 = 2.

What is the Least Perfect Square Divisible by 8 and 14?

The least number divisible by 8 and 14 = LCM(8, 14)
LCM of 8 and 14 = 2 × 2 × 2 × 7 [Incomplete pair(s): 2, 7]
⇒ Least perfect square divisible by each 8 and 14 = LCM(8, 14) × 2 × 7 = 784 [Square root of 784 = √784 = ±28]
Therefore, 784 is the required number.

Which of the following is the LCM of 8 and 14? 24, 56, 36, 16

The value of LCM of 8, 14 is the smallest common multiple of 8 and 14. The number satisfying the given condition is 56.

What are the Methods to Find LCM of 8 and 14?

The commonly used methods to find the LCM of 8 and 14 are:

• Listing Multiples
• Division Method
• Prime Factorization Method