LCM of 80 and 120
LCM of 80 and 120 is the smallest number among all common multiples of 80 and 120. The first few multiples of 80 and 120 are (80, 160, 240, 320, 400, 480, 560, . . . ) and (120, 240, 360, 480, 600, 720, . . . ) respectively. There are 3 commonly used methods to find LCM of 80 and 120  by division method, by listing multiples, and by prime factorization.
1.  LCM of 80 and 120 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 80 and 120?
Answer: LCM of 80 and 120 is 240.
Explanation:
The LCM of two nonzero integers, x(80) and y(120), is the smallest positive integer m(240) that is divisible by both x(80) and y(120) without any remainder.
Methods to Find LCM of 80 and 120
The methods to find the LCM of 80 and 120 are explained below.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 80 and 120 by Prime Factorization
Prime factorization of 80 and 120 is (2 × 2 × 2 × 2 × 5) = 2^{4} × 5^{1} and (2 × 2 × 2 × 3 × 5) = 2^{3} × 3^{1} × 5^{1} respectively. LCM of 80 and 120 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{4} × 3^{1} × 5^{1} = 240.
Hence, the LCM of 80 and 120 by prime factorization is 240.
LCM of 80 and 120 by Listing Multiples
To calculate the LCM of 80 and 120 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 80 (80, 160, 240, 320, 400, 480, 560, . . . ) and 120 (120, 240, 360, 480, 600, 720, . . . . )
 Step 2: The common multiples from the multiples of 80 and 120 are 240, 480, . . .
 Step 3: The smallest common multiple of 80 and 120 is 240.
∴ The least common multiple of 80 and 120 = 240.
LCM of 80 and 120 by Division Method
To calculate the LCM of 80 and 120 by the division method, we will divide the numbers(80, 120) by their prime factors (preferably common). The product of these divisors gives the LCM of 80 and 120.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 80 and 120. Write this prime number(2) on the left of the given numbers(80 and 120), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (80, 120) 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 80 and 120 is the product of all prime numbers on the left, i.e. LCM(80, 120) by division method = 2 × 2 × 2 × 2 × 3 × 5 = 240.
☛ Also Check:
 LCM of 5, 10 and 15  30
 LCM of 2, 5 and 10  10
 LCM of 35 and 55  385
 LCM of 4 and 10  20
 LCM of 20 and 50  100
 LCM of 36 and 72  72
 LCM of 20 and 30  60
LCM of 80 and 120 Examples

Example 1: Verify the relationship between GCF and LCM of 80 and 120.
Solution:
The relation between GCF and LCM of 80 and 120 is given as,
LCM(80, 120) × GCF(80, 120) = Product of 80, 120
Prime factorization of 80 and 120 is given as, 80 = (2 × 2 × 2 × 2 × 5) = 2^{4} × 5^{1} and 120 = (2 × 2 × 2 × 3 × 5) = 2^{3} × 3^{1} × 5^{1}
LCM(80, 120) = 240
GCF(80, 120) = 40
LHS = LCM(80, 120) × GCF(80, 120) = 240 × 40 = 9600
RHS = Product of 80, 120 = 80 × 120 = 9600
⇒ LHS = RHS = 9600
Hence, verified. 
Example 2: The product of two numbers is 9600. If their GCD is 40, what is their LCM?
Solution:
Given: GCD = 40
product of numbers = 9600
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 9600/40
Therefore, the LCM is 240.
The probable combination for the given case is LCM(80, 120) = 240. 
Example 3: Find the smallest number that is divisible by 80 and 120 exactly.
Solution:
The smallest number that is divisible by 80 and 120 exactly is their LCM.
⇒ Multiples of 80 and 120: Multiples of 80 = 80, 160, 240, 320, 400, 480, . . . .
 Multiples of 120 = 120, 240, 360, 480, 600, 720, . . . .
Therefore, the LCM of 80 and 120 is 240.
FAQs on LCM of 80 and 120
What is the LCM of 80 and 120?
The LCM of 80 and 120 is 240. To find the least common multiple of 80 and 120, we need to find the multiples of 80 and 120 (multiples of 80 = 80, 160, 240, 320; multiples of 120 = 120, 240, 360, 480) and choose the smallest multiple that is exactly divisible by 80 and 120, i.e., 240.
Which of the following is the LCM of 80 and 120? 27, 5, 32, 240
The value of LCM of 80, 120 is the smallest common multiple of 80 and 120. The number satisfying the given condition is 240.
What are the Methods to Find LCM of 80 and 120?
The commonly used methods to find the LCM of 80 and 120 are:
 Division Method
 Listing Multiples
 Prime Factorization Method
If the LCM of 120 and 80 is 240, Find its GCF.
LCM(120, 80) × GCF(120, 80) = 120 × 80
Since the LCM of 120 and 80 = 240
⇒ 240 × GCF(120, 80) = 9600
Therefore, the GCF = 9600/240 = 40.
What is the Least Perfect Square Divisible by 80 and 120?
The least number divisible by 80 and 120 = LCM(80, 120)
LCM of 80 and 120 = 2 × 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 3, 5]
⇒ Least perfect square divisible by each 80 and 120 = LCM(80, 120) × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.
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