LCM of 14 and 21

LCM of 14 and 21 is the smallest number among all common multiples of 14 and 21. The first few multiples of 14 and 21 are (14, 28, 42, 56, . . . ) and (21, 42, 63, 84, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 21 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 14 and 21 is 42.

Explanation:

The LCM of two non-zero integers, x(14) and y(21), is the smallest positive integer m(42) that is divisible by both x(14) and y(21) without any remainder.

Let's look at the different methods for finding the LCM of 14 and 21.

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

LCM of 14 and 21 by Prime Factorization

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

LCM of 14 and 21 by Listing Multiples

To calculate the LCM of 14 and 21 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 21 (21, 42, 63, 84, . . . . )
• Step 2: The common multiples from the multiples of 14 and 21 are 42, 84, . . .
• Step 3: The smallest common multiple of 14 and 21 is 42.

∴ The least common multiple of 14 and 21 = 42.

LCM of 14 and 21 by Division Method

To calculate the LCM of 14 and 21 by the division method, we will divide the numbers(14, 21) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 21.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 21. Write this prime number(2) on the left of the given numbers(14 and 21), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (14, 21) 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 21 is the product of all prime numbers on the left, i.e. LCM(14, 21) by division method = 2 × 3 × 7 = 42.

☛ Also Check:

• LCM of 80 and 120 - 240
• LCM of 8 and 9 - 72
• LCM of 8 and 64 - 64
• LCM of 8 and 56 - 56
• LCM of 8 and 42 - 168
• LCM of 8 and 36 - 72
• LCM of 8 and 32 - 32

FAQs on LCM of 14 and 21

What is the LCM of 14 and 21?

The LCM of 14 and 21 is 42. To find the least common multiple (LCM) of 14 and 21, we need to find the multiples of 14 and 21 (multiples of 14 = 14, 28, 42, 56; multiples of 21 = 21, 42, 63, 84) and choose the smallest multiple that is exactly divisible by 14 and 21, i.e., 42.

Which of the following is the LCM of 14 and 21? 11, 3, 12, 42

The value of LCM of 14, 21 is the smallest common multiple of 14 and 21. The number satisfying the given condition is 42.

How to Find the LCM of 14 and 21 by Prime Factorization?

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

What is the Least Perfect Square Divisible by 14 and 21?

The least number divisible by 14 and 21 = LCM(14, 21)
LCM of 14 and 21 = 2 × 3 × 7 [Incomplete pair(s): 2, 3, 7]
⇒ Least perfect square divisible by each 14 and 21 = LCM(14, 21) × 2 × 3 × 7 = 1764 [Square root of 1764 = √1764 = ±42]
Therefore, 1764 is the required number.

If the LCM of 21 and 14 is 42, Find its GCF.

LCM(21, 14) × GCF(21, 14) = 21 × 14
Since the LCM of 21 and 14 = 42
⇒ 42 × GCF(21, 14) = 294
Therefore, the GCF = 294/42 = 7.