LCM of 10 and 50

LCM of 10 and 50 is the smallest number among all common multiples of 10 and 50. The first few multiples of 10 and 50 are (10, 20, 30, 40, 50, 60, . . . ) and (50, 100, 150, 200, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 50 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 10 and 50 is 50.

Explanation:

The LCM of two non-zero integers, x(10) and y(50), is the smallest positive integer m(50) that is divisible by both x(10) and y(50) without any remainder.

Let's look at the different methods for finding the LCM of 10 and 50.

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

LCM of 10 and 50 by Prime Factorization

Prime factorization of 10 and 50 is (2 × 5) = 2¹ × 5¹ and (2 × 5 × 5) = 2¹ × 5² respectively. LCM of 10 and 50 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 5² = 50.
Hence, the LCM of 10 and 50 by prime factorization is 50.

LCM of 10 and 50 by Division Method

To calculate the LCM of 10 and 50 by the division method, we will divide the numbers(10, 50) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 50.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 50. Write this prime number(2) on the left of the given numbers(10 and 50), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (10, 50) 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 50 is the product of all prime numbers on the left, i.e. LCM(10, 50) by division method = 2 × 5 × 5 = 50.

LCM of 10 and 50 by Listing Multiples

To calculate the LCM of 10 and 50 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, 60, . . . ) and 50 (50, 100, 150, 200, . . . . )
• Step 2: The common multiples from the multiples of 10 and 50 are 50, 100, . . .
• Step 3: The smallest common multiple of 10 and 50 is 50.

∴ The least common multiple of 10 and 50 = 50.

☛ Also Check:

• LCM of 48 and 120 - 240
• LCM of 48 and 108 - 432
• LCM of 45 and 99 - 495
• LCM of 45 and 90 - 90
• LCM of 45 and 86 - 3870
• LCM of 45 and 75 - 225
• LCM of 45 and 72 - 360

FAQs on LCM of 10 and 50

What is the LCM of 10 and 50?

The LCM of 10 and 50 is 50. To find the LCM of 10 and 50, we need to find the multiples of 10 and 50 (multiples of 10 = 10, 20, 30, 40 . . . . 50; multiples of 50 = 50, 100, 150, 200) and choose the smallest multiple that is exactly divisible by 10 and 50, i.e., 50.

If the LCM of 50 and 10 is 50, Find its GCF.

LCM(50, 10) × GCF(50, 10) = 50 × 10
Since the LCM of 50 and 10 = 50
⇒ 50 × GCF(50, 10) = 500
Therefore, the greatest common factor (GCF) = 500/50 = 10.

What is the Relation Between GCF and LCM of 10, 50?

The following equation can be used to express the relation between GCF and LCM of 10 and 50, i.e. GCF × LCM = 10 × 50.

What are the Methods to Find LCM of 10 and 50?

The commonly used methods to find the LCM of 10 and 50 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

How to Find the LCM of 10 and 50 by Prime Factorization?

To find the LCM of 10 and 50 using prime factorization, we will find the prime factors, (10 = 2 × 5) and (50 = 2 × 5 × 5). LCM of 10 and 50 is the product of prime factors raised to their respective highest exponent among the numbers 10 and 50.
⇒ LCM of 10, 50 = 2¹ × 5² = 50.