LCM of 207 and 138

LCM of 207 and 138 is the smallest number among all common multiples of 207 and 138. The first few multiples of 207 and 138 are (207, 414, 621, 828, . . . ) and (138, 276, 414, 552, 690, . . . ) respectively. There are 3 commonly used methods to find LCM of 207 and 138 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 207 and 138 is 414.

Explanation:

The LCM of two non-zero integers, x(207) and y(138), is the smallest positive integer m(414) that is divisible by both x(207) and y(138) without any remainder.

The methods to find the LCM of 207 and 138 are explained below.

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

LCM of 207 and 138 by Listing Multiples

To calculate the LCM of 207 and 138 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 207 (207, 414, 621, 828, . . . ) and 138 (138, 276, 414, 552, 690, . . . . )
• Step 2: The common multiples from the multiples of 207 and 138 are 414, 828, . . .
• Step 3: The smallest common multiple of 207 and 138 is 414.

∴ The least common multiple of 207 and 138 = 414.

LCM of 207 and 138 by Prime Factorization

Prime factorization of 207 and 138 is (3 × 3 × 23) = 3² × 23¹ and (2 × 3 × 23) = 2¹ × 3¹ × 23¹ respectively. LCM of 207 and 138 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 23¹ = 414.
Hence, the LCM of 207 and 138 by prime factorization is 414.

LCM of 207 and 138 by Division Method

To calculate the LCM of 207 and 138 by the division method, we will divide the numbers(207, 138) by their prime factors (preferably common). The product of these divisors gives the LCM of 207 and 138.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 207 and 138. Write this prime number(2) on the left of the given numbers(207 and 138), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (207, 138) 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 207 and 138 is the product of all prime numbers on the left, i.e. LCM(207, 138) by division method = 2 × 3 × 3 × 23 = 414.

☛ Also Check:

• LCM of 12, 16 and 18 - 144
• LCM of 4, 12 and 20 - 60
• LCM of 60 and 75 - 300
• LCM of 5, 10 and 15 - 30
• LCM of 6, 10 and 12 - 60
• LCM of 56 and 84 - 168
• LCM of 4 and 10 - 20

FAQs on LCM of 207 and 138

What is the LCM of 207 and 138?

The LCM of 207 and 138 is 414. To find the LCM (least common multiple) of 207 and 138, we need to find the multiples of 207 and 138 (multiples of 207 = 207, 414, 621, 828; multiples of 138 = 138, 276, 414, 552) and choose the smallest multiple that is exactly divisible by 207 and 138, i.e., 414.

How to Find the LCM of 207 and 138 by Prime Factorization?

To find the LCM of 207 and 138 using prime factorization, we will find the prime factors, (207 = 3 × 3 × 23) and (138 = 2 × 3 × 23). LCM of 207 and 138 is the product of prime factors raised to their respective highest exponent among the numbers 207 and 138.
⇒ LCM of 207, 138 = 2¹ × 3² × 23¹ = 414.

What are the Methods to Find LCM of 207 and 138?

The commonly used methods to find the LCM of 207 and 138 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

If the LCM of 138 and 207 is 414, Find its GCF.

LCM(138, 207) × GCF(138, 207) = 138 × 207
Since the LCM of 138 and 207 = 414
⇒ 414 × GCF(138, 207) = 28566
Therefore, the greatest common factor = 28566/414 = 69.

What is the Least Perfect Square Divisible by 207 and 138?

The least number divisible by 207 and 138 = LCM(207, 138)
LCM of 207 and 138 = 2 × 3 × 3 × 23 [Incomplete pair(s): 2, 23]
⇒ Least perfect square divisible by each 207 and 138 = LCM(207, 138) × 2 × 23 = 19044 [Square root of 19044 = √19044 = ±138]
Therefore, 19044 is the required number.