LCM of 150 and 500

LCM of 150 and 500 is the smallest number among all common multiples of 150 and 500. The first few multiples of 150 and 500 are (150, 300, 450, 600, . . . ) and (500, 1000, 1500, 2000, . . . ) respectively. There are 3 commonly used methods to find LCM of 150 and 500 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 150 and 500 is 1500.

Explanation:

The LCM of two non-zero integers, x(150) and y(500), is the smallest positive integer m(1500) that is divisible by both x(150) and y(500) without any remainder.

Let's look at the different methods for finding the LCM of 150 and 500.

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

LCM of 150 and 500 by Division Method

To calculate the LCM of 150 and 500 by the division method, we will divide the numbers(150, 500) by their prime factors (preferably common). The product of these divisors gives the LCM of 150 and 500.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 150 and 500. Write this prime number(2) on the left of the given numbers(150 and 500), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (150, 500) 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 150 and 500 is the product of all prime numbers on the left, i.e. LCM(150, 500) by division method = 2 × 2 × 3 × 5 × 5 × 5 = 1500.

LCM of 150 and 500 by Prime Factorization

Prime factorization of 150 and 500 is (2 × 3 × 5 × 5) = 2¹ × 3¹ × 5² and (2 × 2 × 5 × 5 × 5) = 2² × 5³ respectively. LCM of 150 and 500 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5³ = 1500.
Hence, the LCM of 150 and 500 by prime factorization is 1500.

LCM of 150 and 500 by Listing Multiples

To calculate the LCM of 150 and 500 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 150 (150, 300, 450, 600, . . . ) and 500 (500, 1000, 1500, 2000, . . . . )
• Step 2: The common multiples from the multiples of 150 and 500 are 1500, 3000, . . .
• Step 3: The smallest common multiple of 150 and 500 is 1500.

∴ The least common multiple of 150 and 500 = 1500.

☛ Also Check:

• LCM of 6, 12 and 15 - 60
• LCM of 3, 6 and 8 - 24
• LCM of 8, 12 and 15 - 120
• LCM of 27 and 45 - 135
• LCM of 30 and 60 - 60
• LCM of 8, 15 and 21 - 840
• LCM of 18 and 30 - 90

FAQs on LCM of 150 and 500

What is the LCM of 150 and 500?

The LCM of 150 and 500 is 1500. To find the least common multiple of 150 and 500, we need to find the multiples of 150 and 500 (multiples of 150 = 150, 300, 450, 600 . . . . 1500; multiples of 500 = 500, 1000, 1500, 2000) and choose the smallest multiple that is exactly divisible by 150 and 500, i.e., 1500.

What are the Methods to Find LCM of 150 and 500?

The commonly used methods to find the LCM of 150 and 500 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

If the LCM of 500 and 150 is 1500, Find its GCF.

LCM(500, 150) × GCF(500, 150) = 500 × 150
Since the LCM of 500 and 150 = 1500
⇒ 1500 × GCF(500, 150) = 75000
Therefore, the greatest common factor = 75000/1500 = 50.

How to Find the LCM of 150 and 500 by Prime Factorization?

To find the LCM of 150 and 500 using prime factorization, we will find the prime factors, (150 = 2 × 3 × 5 × 5) and (500 = 2 × 2 × 5 × 5 × 5). LCM of 150 and 500 is the product of prime factors raised to their respective highest exponent among the numbers 150 and 500.
⇒ LCM of 150, 500 = 2² × 3¹ × 5³ = 1500.

What is the Relation Between GCF and LCM of 150, 500?

The following equation can be used to express the relation between GCF and LCM of 150 and 500, i.e. GCF × LCM = 150 × 500.