LCM of 75 and 80

LCM of 75 and 80 is the smallest number among all common multiples of 75 and 80. The first few multiples of 75 and 80 are (75, 150, 225, 300, 375, . . . ) and (80, 160, 240, 320, . . . ) respectively. There are 3 commonly used methods to find LCM of 75 and 80 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 75 and 80 is 1200.

Explanation:

The LCM of two non-zero integers, x(75) and y(80), is the smallest positive integer m(1200) that is divisible by both x(75) and y(80) without any remainder.

The methods to find the LCM of 75 and 80 are explained below.

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

LCM of 75 and 80 by Prime Factorization

Prime factorization of 75 and 80 is (3 × 5 × 5) = 3¹ × 5² and (2 × 2 × 2 × 2 × 5) = 2⁴ × 5¹ respectively. LCM of 75 and 80 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ × 5² = 1200.
Hence, the LCM of 75 and 80 by prime factorization is 1200.

LCM of 75 and 80 by Division Method

To calculate the LCM of 75 and 80 by the division method, we will divide the numbers(75, 80) by their prime factors (preferably common). The product of these divisors gives the LCM of 75 and 80.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 75 and 80. Write this prime number(2) on the left of the given numbers(75 and 80), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (75, 80) 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 75 and 80 is the product of all prime numbers on the left, i.e. LCM(75, 80) by division method = 2 × 2 × 2 × 2 × 3 × 5 × 5 = 1200.

LCM of 75 and 80 by Listing Multiples

To calculate the LCM of 75 and 80 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 75 (75, 150, 225, 300, 375, . . . ) and 80 (80, 160, 240, 320, . . . . )
• Step 2: The common multiples from the multiples of 75 and 80 are 1200, 2400, . . .
• Step 3: The smallest common multiple of 75 and 80 is 1200.

∴ The least common multiple of 75 and 80 = 1200.

☛ Also Check:

• LCM of 144 and 180 - 720
• LCM of 45 and 90 - 90
• LCM of 120 and 90 - 360
• LCM of 30 and 50 - 150
• LCM of 3, 9 and 18 - 18
• LCM of 6 and 15 - 30
• LCM of 4 and 20 - 20

FAQs on LCM of 75 and 80

What is the LCM of 75 and 80?

The LCM of 75 and 80 is 1200. To find the least common multiple (LCM) of 75 and 80, we need to find the multiples of 75 and 80 (multiples of 75 = 75, 150, 225, 300 . . . . 1200; multiples of 80 = 80, 160, 240, 320 . . . . 1200) and choose the smallest multiple that is exactly divisible by 75 and 80, i.e., 1200.

What is the Relation Between GCF and LCM of 75, 80?

The following equation can be used to express the relation between GCF and LCM of 75 and 80, i.e. GCF × LCM = 75 × 80.

What is the Least Perfect Square Divisible by 75 and 80?

The least number divisible by 75 and 80 = LCM(75, 80)
LCM of 75 and 80 = 2 × 2 × 2 × 2 × 3 × 5 × 5 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 75 and 80 = LCM(75, 80) × 3 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

What are the Methods to Find LCM of 75 and 80?

The commonly used methods to find the LCM of 75 and 80 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

If the LCM of 80 and 75 is 1200, Find its GCF.

LCM(80, 75) × GCF(80, 75) = 80 × 75
Since the LCM of 80 and 75 = 1200
⇒ 1200 × GCF(80, 75) = 6000
Therefore, the greatest common factor (GCF) = 6000/1200 = 5.