LCM of 150 and 180
LCM of 150 and 180 is the smallest number among all common multiples of 150 and 180. The first few multiples of 150 and 180 are (150, 300, 450, 600, . . . ) and (180, 360, 540, 720, 900, 1080, . . . ) respectively. There are 3 commonly used methods to find LCM of 150 and 180  by division method, by prime factorization, and by listing multiples.
1.  LCM of 150 and 180 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 150 and 180?
Answer: LCM of 150 and 180 is 900.
Explanation:
The LCM of two nonzero integers, x(150) and y(180), is the smallest positive integer m(900) that is divisible by both x(150) and y(180) without any remainder.
Methods to Find LCM of 150 and 180
The methods to find the LCM of 150 and 180 are explained below.
 By Listing Multiples
 By Division Method
 By Prime Factorization Method
LCM of 150 and 180 by Listing Multiples
To calculate the LCM of 150 and 180 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 150 (150, 300, 450, 600, . . . ) and 180 (180, 360, 540, 720, 900, 1080, . . . . )
 Step 2: The common multiples from the multiples of 150 and 180 are 900, 1800, . . .
 Step 3: The smallest common multiple of 150 and 180 is 900.
∴ The least common multiple of 150 and 180 = 900.
LCM of 150 and 180 by Division Method
To calculate the LCM of 150 and 180 by the division method, we will divide the numbers(150, 180) by their prime factors (preferably common). The product of these divisors gives the LCM of 150 and 180.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 150 and 180. Write this prime number(2) on the left of the given numbers(150 and 180), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (150, 180) 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 150 and 180 is the product of all prime numbers on the left, i.e. LCM(150, 180) by division method = 2 × 2 × 3 × 3 × 5 × 5 = 900.
LCM of 150 and 180 by Prime Factorization
Prime factorization of 150 and 180 is (2 × 3 × 5 × 5) = 2^{1} × 3^{1} × 5^{2} and (2 × 2 × 3 × 3 × 5) = 2^{2} × 3^{2} × 5^{1} respectively. LCM of 150 and 180 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{2} × 5^{2} = 900.
Hence, the LCM of 150 and 180 by prime factorization is 900.
☛ Also Check:
 LCM of 72 and 84  504
 LCM of 63 and 21  63
 LCM of 60 and 90  180
 LCM of 186 and 403  2418
 LCM of 7, 14 and 21  42
 LCM of 2 and 13  26
 LCM of 2, 4, 6, 8, 10 and 12  120
LCM of 150 and 180 Examples

Example 1: The GCD and LCM of two numbers are 30 and 900 respectively. If one number is 150, find the other number.
Solution:
Let the other number be a.
∵ GCD × LCM = 150 × a
⇒ a = (GCD × LCM)/150
⇒ a = (30 × 900)/150
⇒ a = 180
Therefore, the other number is 180. 
Example 2: Verify the relationship between GCF and LCM of 150 and 180.
Solution:
The relation between GCF and LCM of 150 and 180 is given as,
LCM(150, 180) × GCF(150, 180) = Product of 150, 180
Prime factorization of 150 and 180 is given as, 150 = (2 × 3 × 5 × 5) = 2^{1} × 3^{1} × 5^{2} and 180 = (2 × 2 × 3 × 3 × 5) = 2^{2} × 3^{2} × 5^{1}
LCM(150, 180) = 900
GCF(150, 180) = 30
LHS = LCM(150, 180) × GCF(150, 180) = 900 × 30 = 27000
RHS = Product of 150, 180 = 150 × 180 = 27000
⇒ LHS = RHS = 27000
Hence, verified. 
Example 3: Find the smallest number that is divisible by 150 and 180 exactly.
Solution:
The smallest number that is divisible by 150 and 180 exactly is their LCM.
⇒ Multiples of 150 and 180: Multiples of 150 = 150, 300, 450, 600, 750, 900, 1050, . . . .
 Multiples of 180 = 180, 360, 540, 720, 900, 1080, 1260, . . . .
Therefore, the LCM of 150 and 180 is 900.
FAQs on LCM of 150 and 180
What is the LCM of 150 and 180?
The LCM of 150 and 180 is 900. To find the least common multiple of 150 and 180, we need to find the multiples of 150 and 180 (multiples of 150 = 150, 300, 450, 600 . . . . 900; multiples of 180 = 180, 360, 540, 720 . . . . 900) and choose the smallest multiple that is exactly divisible by 150 and 180, i.e., 900.
How to Find the LCM of 150 and 180 by Prime Factorization?
To find the LCM of 150 and 180 using prime factorization, we will find the prime factors, (150 = 2 × 3 × 5 × 5) and (180 = 2 × 2 × 3 × 3 × 5). LCM of 150 and 180 is the product of prime factors raised to their respective highest exponent among the numbers 150 and 180.
⇒ LCM of 150, 180 = 2^{2} × 3^{2} × 5^{2} = 900.
What is the Least Perfect Square Divisible by 150 and 180?
The least number divisible by 150 and 180 = LCM(150, 180)
LCM of 150 and 180 = 2 × 2 × 3 × 3 × 5 × 5 [No incomplete pair]
⇒ Least perfect square divisible by each 150 and 180 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.
What is the Relation Between GCF and LCM of 150, 180?
The following equation can be used to express the relation between GCF and LCM of 150 and 180, i.e. GCF × LCM = 150 × 180.
If the LCM of 180 and 150 is 900, Find its GCF.
LCM(180, 150) × GCF(180, 150) = 180 × 150
Since the LCM of 180 and 150 = 900
⇒ 900 × GCF(180, 150) = 27000
Therefore, the GCF = 27000/900 = 30.
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