LCM of 3 and 14

LCM of 3 and 14 is the smallest number among all common multiples of 3 and 14. The first few multiples of 3 and 14 are (3, 6, 9, 12, 15, . . . ) and (14, 28, 42, 56, 70, 84, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 14 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 3 and 14 is 42.

Explanation:

The LCM of two non-zero integers, x(3) and y(14), is the smallest positive integer m(42) that is divisible by both x(3) and y(14) without any remainder.

Let's look at the different methods for finding the LCM of 3 and 14.

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

LCM of 3 and 14 by Prime Factorization

Prime factorization of 3 and 14 is (3) = 3¹ and (2 × 7) = 2¹ × 7¹ respectively. LCM of 3 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 3 and 14 by prime factorization is 42.

LCM of 3 and 14 by Listing Multiples

To calculate the LCM of 3 and 14 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, . . . ) and 14 (14, 28, 42, 56, 70, 84, . . . . )
• Step 2: The common multiples from the multiples of 3 and 14 are 42, 84, . . .
• Step 3: The smallest common multiple of 3 and 14 is 42.

∴ The least common multiple of 3 and 14 = 42.

LCM of 3 and 14 by Division Method

To calculate the LCM of 3 and 14 by the division method, we will divide the numbers(3, 14) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 14.

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

☛ Also Check:

• LCM of 30, 45 and 60 - 180
• LCM of 14 and 28 - 28
• LCM of 35, 12 and 70 - 420
• LCM of 15 and 24 - 120
• LCM of 16 and 32 - 32
• LCM of 10, 20 and 30 - 60
• LCM of 5 and 16 - 80

FAQs on LCM of 3 and 14

What is the LCM of 3 and 14?

The LCM of 3 and 14 is 42. To find the least common multiple (LCM) of 3 and 14, we need to find the multiples of 3 and 14 (multiples of 3 = 3, 6, 9, 12 . . . . 42; multiples of 14 = 14, 28, 42, 56) and choose the smallest multiple that is exactly divisible by 3 and 14, i.e., 42.

What is the Relation Between GCF and LCM of 3, 14?

The following equation can be used to express the relation between GCF and LCM of 3 and 14, i.e. GCF × LCM = 3 × 14.

If the LCM of 14 and 3 is 42, Find its GCF.

LCM(14, 3) × GCF(14, 3) = 14 × 3
Since the LCM of 14 and 3 = 42
⇒ 42 × GCF(14, 3) = 42
Therefore, the GCF (greatest common factor) = 42/42 = 1.

How to Find the LCM of 3 and 14 by Prime Factorization?

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

What are the Methods to Find LCM of 3 and 14?

The commonly used methods to find the LCM of 3 and 14 are:

• Prime Factorization Method
• Division Method
• Listing Multiples