LCM of 50 and 75

LCM of 50 and 75 is the smallest number among all common multiples of 50 and 75. The first few multiples of 50 and 75 are (50, 100, 150, 200, 250, 300, 350, . . . ) and (75, 150, 225, 300, . . . ) respectively. There are 3 commonly used methods to find LCM of 50 and 75 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 50 and 75 is 150.

Explanation:

The LCM of two non-zero integers, x(50) and y(75), is the smallest positive integer m(150) that is divisible by both x(50) and y(75) without any remainder.

The methods to find the LCM of 50 and 75 are explained below.

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

LCM of 50 and 75 by Listing Multiples

To calculate the LCM of 50 and 75 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 50 (50, 100, 150, 200, 250, 300, 350, . . . ) and 75 (75, 150, 225, 300, . . . . )
• Step 2: The common multiples from the multiples of 50 and 75 are 150, 300, . . .
• Step 3: The smallest common multiple of 50 and 75 is 150.

∴ The least common multiple of 50 and 75 = 150.

LCM of 50 and 75 by Division Method

To calculate the LCM of 50 and 75 by the division method, we will divide the numbers(50, 75) by their prime factors (preferably common). The product of these divisors gives the LCM of 50 and 75.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 50 and 75. Write this prime number(2) on the left of the given numbers(50 and 75), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (50, 75) 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 50 and 75 is the product of all prime numbers on the left, i.e. LCM(50, 75) by division method = 2 × 3 × 5 × 5 = 150.

LCM of 50 and 75 by Prime Factorization

Prime factorization of 50 and 75 is (2 × 5 × 5) = 2¹ × 5² and (3 × 5 × 5) = 3¹ × 5² respectively. LCM of 50 and 75 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 5² = 150.
Hence, the LCM of 50 and 75 by prime factorization is 150.

☛ Also Check:

• LCM of 2, 5 and 8 - 40
• LCM of 11 and 12 - 132
• LCM of 63 and 105 - 315
• LCM of 25 and 36 - 900
• LCM of 16 and 30 - 240
• LCM of 14 and 22 - 154
• LCM of 36 and 72 - 72

FAQs on LCM of 50 and 75

What is the LCM of 50 and 75?

The LCM of 50 and 75 is 150. To find the least common multiple of 50 and 75, we need to find the multiples of 50 and 75 (multiples of 50 = 50, 100, 150, 200; multiples of 75 = 75, 150, 225, 300) and choose the smallest multiple that is exactly divisible by 50 and 75, i.e., 150.

How to Find the LCM of 50 and 75 by Prime Factorization?

To find the LCM of 50 and 75 using prime factorization, we will find the prime factors, (50 = 2 × 5 × 5) and (75 = 3 × 5 × 5). LCM of 50 and 75 is the product of prime factors raised to their respective highest exponent among the numbers 50 and 75.
⇒ LCM of 50, 75 = 2¹ × 3¹ × 5² = 150.

What is the Relation Between GCF and LCM of 50, 75?

The following equation can be used to express the relation between GCF and LCM of 50 and 75, i.e. GCF × LCM = 50 × 75.

What are the Methods to Find LCM of 50 and 75?

The commonly used methods to find the LCM of 50 and 75 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

If the LCM of 75 and 50 is 150, Find its GCF.

LCM(75, 50) × GCF(75, 50) = 75 × 50
Since the LCM of 75 and 50 = 150
⇒ 150 × GCF(75, 50) = 3750
Therefore, the GCF (greatest common factor) = 3750/150 = 25.