LCM of 10 and 95

LCM of 10 and 95 is the smallest number among all common multiples of 10 and 95. The first few multiples of 10 and 95 are (10, 20, 30, 40, 50, . . . ) and (95, 190, 285, 380, 475, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 95 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 10 and 95 is 190.

Explanation:

The LCM of two non-zero integers, x(10) and y(95), is the smallest positive integer m(190) that is divisible by both x(10) and y(95) without any remainder.

Let's look at the different methods for finding the LCM of 10 and 95.

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

LCM of 10 and 95 by Listing Multiples

To calculate the LCM of 10 and 95 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 10 (10, 20, 30, 40, 50, . . . ) and 95 (95, 190, 285, 380, 475, . . . . )
• Step 2: The common multiples from the multiples of 10 and 95 are 190, 380, . . .
• Step 3: The smallest common multiple of 10 and 95 is 190.

∴ The least common multiple of 10 and 95 = 190.

LCM of 10 and 95 by Division Method

To calculate the LCM of 10 and 95 by the division method, we will divide the numbers(10, 95) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 95.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 95. Write this prime number(2) on the left of the given numbers(10 and 95), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (10, 95) 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 10 and 95 is the product of all prime numbers on the left, i.e. LCM(10, 95) by division method = 2 × 5 × 19 = 190.

LCM of 10 and 95 by Prime Factorization

Prime factorization of 10 and 95 is (2 × 5) = 2¹ × 5¹ and (5 × 19) = 5¹ × 19¹ respectively. LCM of 10 and 95 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 5¹ × 19¹ = 190.
Hence, the LCM of 10 and 95 by prime factorization is 190.

☛ Also Check:

• LCM of 4 and 9 - 36
• LCM of 4 and 8 - 8
• LCM of 4 and 7 - 28
• LCM of 4 and 6 - 12
• LCM of 4 and 5 - 20
• LCM of 4 and 30 - 60
• LCM of 4 and 24 - 24

FAQs on LCM of 10 and 95

What is the LCM of 10 and 95?

The LCM of 10 and 95 is 190. To find the least common multiple of 10 and 95, we need to find the multiples of 10 and 95 (multiples of 10 = 10, 20, 30, 40 . . . . 190; multiples of 95 = 95, 190, 285, 380) and choose the smallest multiple that is exactly divisible by 10 and 95, i.e., 190.

What is the Relation Between GCF and LCM of 10, 95?

The following equation can be used to express the relation between GCF and LCM of 10 and 95, i.e. GCF × LCM = 10 × 95.

What is the Least Perfect Square Divisible by 10 and 95?

The least number divisible by 10 and 95 = LCM(10, 95)
LCM of 10 and 95 = 2 × 5 × 19 [Incomplete pair(s): 2, 5, 19]
⇒ Least perfect square divisible by each 10 and 95 = LCM(10, 95) × 2 × 5 × 19 = 36100 [Square root of 36100 = √36100 = ±190]
Therefore, 36100 is the required number.

If the LCM of 95 and 10 is 190, Find its GCF.

LCM(95, 10) × GCF(95, 10) = 95 × 10
Since the LCM of 95 and 10 = 190
⇒ 190 × GCF(95, 10) = 950
Therefore, the greatest common factor (GCF) = 950/190 = 5.

How to Find the LCM of 10 and 95 by Prime Factorization?

To find the LCM of 10 and 95 using prime factorization, we will find the prime factors, (10 = 2 × 5) and (95 = 5 × 19). LCM of 10 and 95 is the product of prime factors raised to their respective highest exponent among the numbers 10 and 95.
⇒ LCM of 10, 95 = 2¹ × 5¹ × 19¹ = 190.