LCM of 105 and 195

LCM of 105 and 195 is the smallest number among all common multiples of 105 and 195. The first few multiples of 105 and 195 are (105, 210, 315, 420, 525, 630, 735, . . . ) and (195, 390, 585, 780, . . . ) respectively. There are 3 commonly used methods to find LCM of 105 and 195 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 105 and 195 is 1365.

Explanation:

The LCM of two non-zero integers, x(105) and y(195), is the smallest positive integer m(1365) that is divisible by both x(105) and y(195) without any remainder.

Let's look at the different methods for finding the LCM of 105 and 195.

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

LCM of 105 and 195 by Division Method

To calculate the LCM of 105 and 195 by the division method, we will divide the numbers(105, 195) by their prime factors (preferably common). The product of these divisors gives the LCM of 105 and 195.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 105 and 195. Write this prime number(3) on the left of the given numbers(105 and 195), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (105, 195) is a multiple of 3, divide it by 3 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 105 and 195 is the product of all prime numbers on the left, i.e. LCM(105, 195) by division method = 3 × 5 × 7 × 13 = 1365.

LCM of 105 and 195 by Prime Factorization

Prime factorization of 105 and 195 is (3 × 5 × 7) = 3¹ × 5¹ × 7¹ and (3 × 5 × 13) = 3¹ × 5¹ × 13¹ respectively. LCM of 105 and 195 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3¹ × 5¹ × 7¹ × 13¹ = 1365.
Hence, the LCM of 105 and 195 by prime factorization is 1365.

LCM of 105 and 195 by Listing Multiples

To calculate the LCM of 105 and 195 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 105 (105, 210, 315, 420, 525, 630, 735, . . . ) and 195 (195, 390, 585, 780, . . . . )
• Step 2: The common multiples from the multiples of 105 and 195 are 1365, 2730, . . .
• Step 3: The smallest common multiple of 105 and 195 is 1365.

∴ The least common multiple of 105 and 195 = 1365.

☛ Also Check:

• LCM of 36 and 72 - 72
• LCM of 36 and 64 - 576
• LCM of 36 and 63 - 252
• LCM of 36 and 60 - 180
• LCM of 36 and 54 - 108
• LCM of 36 and 48 - 144
• LCM of 36 and 45 - 180

FAQs on LCM of 105 and 195

What is the LCM of 105 and 195?

The LCM of 105 and 195 is 1365. To find the least common multiple (LCM) of 105 and 195, we need to find the multiples of 105 and 195 (multiples of 105 = 105, 210, 315, 420 . . . . 1365; multiples of 195 = 195, 390, 585, 780 . . . . 1365) and choose the smallest multiple that is exactly divisible by 105 and 195, i.e., 1365.

If the LCM of 195 and 105 is 1365, Find its GCF.

LCM(195, 105) × GCF(195, 105) = 195 × 105
Since the LCM of 195 and 105 = 1365
⇒ 1365 × GCF(195, 105) = 20475
Therefore, the greatest common factor (GCF) = 20475/1365 = 15.

What are the Methods to Find LCM of 105 and 195?

The commonly used methods to find the LCM of 105 and 195 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

Which of the following is the LCM of 105 and 195? 45, 5, 2, 1365

The value of LCM of 105, 195 is the smallest common multiple of 105 and 195. The number satisfying the given condition is 1365.

What is the Relation Between GCF and LCM of 105, 195?

The following equation can be used to express the relation between GCF and LCM of 105 and 195, i.e. GCF × LCM = 105 × 195.