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.
1.  LCM of 75 and 80 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 75 and 80?
Answer: LCM of 75 and 80 is 1200.
Explanation:
The LCM of two nonzero 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.
Methods to Find LCM of 75 and 80
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) = 3^{1} × 5^{2} and (2 × 2 × 2 × 2 × 5) = 2^{4} × 5^{1} respectively. LCM of 75 and 80 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{4} × 3^{1} × 5^{2} = 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
LCM of 75 and 80 Examples

Example 1: Find the smallest number that is divisible by 75 and 80 exactly.
Solution:
The value of LCM(75, 80) will be the smallest number that is exactly divisible by 75 and 80.
⇒ Multiples of 75 and 80: Multiples of 75 = 75, 150, 225, 300, 375, 450, 525, 600, 675, 750, . . . ., 1050, 1125, 1200, . . . .
 Multiples of 80 = 80, 160, 240, 320, 400, 480, 560, 640, 720, 800, . . . ., 1040, 1120, 1200, . . . .
Therefore, the LCM of 75 and 80 is 1200.

Example 2: The GCD and LCM of two numbers are 5 and 1200 respectively. If one number is 80, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 80 × b
⇒ b = (GCD × LCM)/80
⇒ b = (5 × 1200)/80
⇒ b = 75
Therefore, the other number is 75. 
Example 3: The product of two numbers is 6000. If their GCD is 5, what is their LCM?
Solution:
Given: GCD = 5
product of numbers = 6000
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 6000/5
Therefore, the LCM is 1200.
The probable combination for the given case is LCM(75, 80) = 1200.
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.
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