LCM of 14 and 24

LCM of 14 and 24 is the smallest number among all common multiples of 14 and 24. The first few multiples of 14 and 24 are (14, 28, 42, 56, . . . ) and (24, 48, 72, 96, 120, 144, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 24 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 14 and 24 is 168.

Explanation:

The LCM of two non-zero integers, x(14) and y(24), is the smallest positive integer m(168) that is divisible by both x(14) and y(24) without any remainder.

Let's look at the different methods for finding the LCM of 14 and 24.

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

LCM of 14 and 24 by Prime Factorization

Prime factorization of 14 and 24 is (2 × 7) = 2¹ × 7¹ and (2 × 2 × 2 × 3) = 2³ × 3¹ respectively. LCM of 14 and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 7¹ = 168.
Hence, the LCM of 14 and 24 by prime factorization is 168.

LCM of 14 and 24 by Listing Multiples

To calculate the LCM of 14 and 24 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 14 (14, 28, 42, 56, . . . ) and 24 (24, 48, 72, 96, 120, 144, . . . . )
• Step 2: The common multiples from the multiples of 14 and 24 are 168, 336, . . .
• Step 3: The smallest common multiple of 14 and 24 is 168.

∴ The least common multiple of 14 and 24 = 168.

LCM of 14 and 24 by Division Method

To calculate the LCM of 14 and 24 by the division method, we will divide the numbers(14, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 24.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 24. Write this prime number(2) on the left of the given numbers(14 and 24), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (14, 24) 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 14 and 24 is the product of all prime numbers on the left, i.e. LCM(14, 24) by division method = 2 × 2 × 2 × 3 × 7 = 168.

☛ Also Check:

• LCM of 8 and 15 - 120
• LCM of 8 and 14 - 56
• LCM of 8 and 13 - 104
• LCM of 8 and 12 - 24
• LCM of 8 and 11 - 88
• LCM of 8 and 10 - 40
• LCM of 75 and 80 - 1200

FAQs on LCM of 14 and 24

What is the LCM of 14 and 24?

The LCM of 14 and 24 is 168. To find the least common multiple (LCM) of 14 and 24, we need to find the multiples of 14 and 24 (multiples of 14 = 14, 28, 42, 56 . . . . 168; multiples of 24 = 24, 48, 72, 96 . . . . 168) and choose the smallest multiple that is exactly divisible by 14 and 24, i.e., 168.

What are the Methods to Find LCM of 14 and 24?

The commonly used methods to find the LCM of 14 and 24 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

What is the Relation Between GCF and LCM of 14, 24?

The following equation can be used to express the relation between GCF and LCM of 14 and 24, i.e. GCF × LCM = 14 × 24.

How to Find the LCM of 14 and 24 by Prime Factorization?

To find the LCM of 14 and 24 using prime factorization, we will find the prime factors, (14 = 2 × 7) and (24 = 2 × 2 × 2 × 3). LCM of 14 and 24 is the product of prime factors raised to their respective highest exponent among the numbers 14 and 24.
⇒ LCM of 14, 24 = 2³ × 3¹ × 7¹ = 168.

If the LCM of 24 and 14 is 168, Find its GCF.

LCM(24, 14) × GCF(24, 14) = 24 × 14
Since the LCM of 24 and 14 = 168
⇒ 168 × GCF(24, 14) = 336
Therefore, the GCF = 336/168 = 2.