LCM of 60 and 75

LCM of 60 and 75 is the smallest number among all common multiples of 60 and 75. The first few multiples of 60 and 75 are (60, 120, 180, 240, 300, 360, . . . ) and (75, 150, 225, 300, 375, . . . ) respectively. There are 3 commonly used methods to find LCM of 60 and 75 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 60 and 75 is 300.

Explanation:

The LCM of two non-zero integers, x(60) and y(75), is the smallest positive integer m(300) that is divisible by both x(60) and y(75) without any remainder.

Let's look at the different methods for finding the LCM of 60 and 75.

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

LCM of 60 and 75 by Division Method

To calculate the LCM of 60 and 75 by the division method, we will divide the numbers(60, 75) by their prime factors (preferably common). The product of these divisors gives the LCM of 60 and 75.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 60 and 75. Write this prime number(2) on the left of the given numbers(60 and 75), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (60, 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 60 and 75 is the product of all prime numbers on the left, i.e. LCM(60, 75) by division method = 2 × 2 × 3 × 5 × 5 = 300.

LCM of 60 and 75 by Prime Factorization

Prime factorization of 60 and 75 is (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ and (3 × 5 × 5) = 3¹ × 5² respectively. LCM of 60 and 75 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5² = 300.
Hence, the LCM of 60 and 75 by prime factorization is 300.

LCM of 60 and 75 by Listing Multiples

To calculate the LCM of 60 and 75 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 60 (60, 120, 180, 240, 300, 360, . . . ) and 75 (75, 150, 225, 300, 375, . . . . )
• Step 2: The common multiples from the multiples of 60 and 75 are 300, 600, . . .
• Step 3: The smallest common multiple of 60 and 75 is 300.

∴ The least common multiple of 60 and 75 = 300.

☛ Also Check:

• LCM of 10 and 24 - 120
• LCM of 18 and 20 - 180
• LCM of 18, 24 and 32 - 288
• LCM of 10, 20 and 25 - 100
• LCM of 5, 9 and 15 - 45
• LCM of 25 and 60 - 300
• LCM of 80 and 120 - 240

FAQs on LCM of 60 and 75

What is the LCM of 60 and 75?

The LCM of 60 and 75 is 300. To find the LCM of 60 and 75, we need to find the multiples of 60 and 75 (multiples of 60 = 60, 120, 180, 240 . . . . 300; multiples of 75 = 75, 150, 225, 300) and choose the smallest multiple that is exactly divisible by 60 and 75, i.e., 300.

What are the Methods to Find LCM of 60 and 75?

The commonly used methods to find the LCM of 60 and 75 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

How to Find the LCM of 60 and 75 by Prime Factorization?

To find the LCM of 60 and 75 using prime factorization, we will find the prime factors, (60 = 2 × 2 × 3 × 5) and (75 = 3 × 5 × 5). LCM of 60 and 75 is the product of prime factors raised to their respective highest exponent among the numbers 60 and 75.
⇒ LCM of 60, 75 = 2² × 3¹ × 5² = 300.

What is the Relation Between GCF and LCM of 60, 75?

The following equation can be used to express the relation between GCF and LCM of 60 and 75, i.e. GCF × LCM = 60 × 75.

If the LCM of 75 and 60 is 300, Find its GCF.

LCM(75, 60) × GCF(75, 60) = 75 × 60
Since the LCM of 75 and 60 = 300
⇒ 300 × GCF(75, 60) = 4500
Therefore, the GCF (greatest common factor) = 4500/300 = 15.