LCM of 9 and 14

LCM of 9 and 14 is the smallest number among all common multiples of 9 and 14. The first few multiples of 9 and 14 are (9, 18, 27, 36, 45, 54, . . . ) and (14, 28, 42, 56, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 14 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 9 and 14 is 126.

Explanation:

The LCM of two non-zero integers, x(9) and y(14), is the smallest positive integer m(126) that is divisible by both x(9) and y(14) without any remainder.

The methods to find the LCM of 9 and 14 are explained below.

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

LCM of 9 and 14 by Division Method

To calculate the LCM of 9 and 14 by the division method, we will divide the numbers(9, 14) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 14.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 14. Write this prime number(2) on the left of the given numbers(9 and 14), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (9, 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 9 and 14 is the product of all prime numbers on the left, i.e. LCM(9, 14) by division method = 2 × 3 × 3 × 7 = 126.

LCM of 9 and 14 by Listing Multiples

To calculate the LCM of 9 and 14 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 9 (9, 18, 27, 36, 45, 54, . . . ) and 14 (14, 28, 42, 56, . . . . )
• Step 2: The common multiples from the multiples of 9 and 14 are 126, 252, . . .
• Step 3: The smallest common multiple of 9 and 14 is 126.

∴ The least common multiple of 9 and 14 = 126.

LCM of 9 and 14 by Prime Factorization

Prime factorization of 9 and 14 is (3 × 3) = 3² and (2 × 7) = 2¹ × 7¹ respectively. LCM of 9 and 14 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 7¹ = 126.
Hence, the LCM of 9 and 14 by prime factorization is 126.

☛ Also Check:

• LCM of 35 and 40 - 280
• LCM of 8, 9 and 25 - 1800
• LCM of 8 and 18 - 72
• LCM of 48 and 64 - 192
• LCM of 12 and 35 - 420
• LCM of 7 and 21 - 21
• LCM of 6, 10 and 12 - 60

FAQs on LCM of 9 and 14

What is the LCM of 9 and 14?

The LCM of 9 and 14 is 126. To find the least common multiple (LCM) of 9 and 14, we need to find the multiples of 9 and 14 (multiples of 9 = 9, 18, 27, 36 . . . . 126; multiples of 14 = 14, 28, 42, 56 . . . . 126) and choose the smallest multiple that is exactly divisible by 9 and 14, i.e., 126.

Which of the following is the LCM of 9 and 14? 5, 126, 10, 11

The value of LCM of 9, 14 is the smallest common multiple of 9 and 14. The number satisfying the given condition is 126.

What is the Least Perfect Square Divisible by 9 and 14?

The least number divisible by 9 and 14 = LCM(9, 14)
LCM of 9 and 14 = 2 × 3 × 3 × 7 [Incomplete pair(s): 2, 7]
⇒ Least perfect square divisible by each 9 and 14 = LCM(9, 14) × 2 × 7 = 1764 [Square root of 1764 = √1764 = ±42]
Therefore, 1764 is the required number.

What are the Methods to Find LCM of 9 and 14?

The commonly used methods to find the LCM of 9 and 14 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

If the LCM of 14 and 9 is 126, Find its GCF.

LCM(14, 9) × GCF(14, 9) = 14 × 9
Since the LCM of 14 and 9 = 126
⇒ 126 × GCF(14, 9) = 126
Therefore, the greatest common factor (GCF) = 126/126 = 1.