LCM of 45 and 90
LCM of 45 and 90 is the smallest number among all common multiples of 45 and 90. The first few multiples of 45 and 90 are (45, 90, 135, 180, 225, 270, 315, . . . ) and (90, 180, 270, 360, 450, 540, 630, . . . ) respectively. There are 3 commonly used methods to find LCM of 45 and 90  by division method, by prime factorization, and by listing multiples.
1.  LCM of 45 and 90 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 45 and 90?
Answer: LCM of 45 and 90 is 90.
Explanation:
The LCM of two nonzero integers, x(45) and y(90), is the smallest positive integer m(90) that is divisible by both x(45) and y(90) without any remainder.
Methods to Find LCM of 45 and 90
The methods to find the LCM of 45 and 90 are explained below.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 45 and 90 by Prime Factorization
Prime factorization of 45 and 90 is (3 × 3 × 5) = 3^{2} × 5^{1} and (2 × 3 × 3 × 5) = 2^{1} × 3^{2} × 5^{1} respectively. LCM of 45 and 90 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{2} × 5^{1} = 90.
Hence, the LCM of 45 and 90 by prime factorization is 90.
LCM of 45 and 90 by Listing Multiples
To calculate the LCM of 45 and 90 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 45 (45, 90, 135, 180, 225, 270, 315, . . . ) and 90 (90, 180, 270, 360, 450, 540, 630, . . . . )
 Step 2: The common multiples from the multiples of 45 and 90 are 90, 180, . . .
 Step 3: The smallest common multiple of 45 and 90 is 90.
∴ The least common multiple of 45 and 90 = 90.
LCM of 45 and 90 by Division Method
To calculate the LCM of 45 and 90 by the division method, we will divide the numbers(45, 90) by their prime factors (preferably common). The product of these divisors gives the LCM of 45 and 90.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 45 and 90. Write this prime number(2) on the left of the given numbers(45 and 90), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (45, 90) 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 45 and 90 is the product of all prime numbers on the left, i.e. LCM(45, 90) by division method = 2 × 3 × 3 × 5 = 90.
☛ Also Check:
 LCM of 42 and 72  504
 LCM of 7 and 9  63
 LCM of 36, 42 and 72  504
 LCM of 16 and 22  176
 LCM of 6 and 7  42
 LCM of 30 and 75  150
 LCM of 13 and 14  182
LCM of 45 and 90 Examples

Example 1: Verify the relationship between GCF and LCM of 45 and 90.
Solution:
The relation between GCF and LCM of 45 and 90 is given as,
LCM(45, 90) × GCF(45, 90) = Product of 45, 90
Prime factorization of 45 and 90 is given as, 45 = (3 × 3 × 5) = 3^{2} × 5^{1} and 90 = (2 × 3 × 3 × 5) = 2^{1} × 3^{2} × 5^{1}
LCM(45, 90) = 90
GCF(45, 90) = 45
LHS = LCM(45, 90) × GCF(45, 90) = 90 × 45 = 4050
RHS = Product of 45, 90 = 45 × 90 = 4050
⇒ LHS = RHS = 4050
Hence, verified. 
Example 2: Find the smallest number that is divisible by 45 and 90 exactly.
Solution:
The smallest number that is divisible by 45 and 90 exactly is their LCM.
⇒ Multiples of 45 and 90: Multiples of 45 = 45, 90, 135, 180, 225, 270, 315, . . . .
 Multiples of 90 = 90, 180, 270, 360, 450, 540, 630, . . . .
Therefore, the LCM of 45 and 90 is 90.

Example 3: The product of two numbers is 4050. If their GCD is 45, what is their LCM?
Solution:
Given: GCD = 45
product of numbers = 4050
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 4050/45
Therefore, the LCM is 90.
The probable combination for the given case is LCM(45, 90) = 90.
FAQs on LCM of 45 and 90
What is the LCM of 45 and 90?
The LCM of 45 and 90 is 90. To find the LCM (least common multiple) of 45 and 90, we need to find the multiples of 45 and 90 (multiples of 45 = 45, 90, 135, 180; multiples of 90 = 90, 180, 270, 360) and choose the smallest multiple that is exactly divisible by 45 and 90, i.e., 90.
What are the Methods to Find LCM of 45 and 90?
The commonly used methods to find the LCM of 45 and 90 are:
 Listing Multiples
 Prime Factorization Method
 Division Method
Which of the following is the LCM of 45 and 90? 90, 2, 35, 27
The value of LCM of 45, 90 is the smallest common multiple of 45 and 90. The number satisfying the given condition is 90.
If the LCM of 90 and 45 is 90, Find its GCF.
LCM(90, 45) × GCF(90, 45) = 90 × 45
Since the LCM of 90 and 45 = 90
⇒ 90 × GCF(90, 45) = 4050
Therefore, the GCF (greatest common factor) = 4050/90 = 45.
How to Find the LCM of 45 and 90 by Prime Factorization?
To find the LCM of 45 and 90 using prime factorization, we will find the prime factors, (45 = 3 × 3 × 5) and (90 = 2 × 3 × 3 × 5). LCM of 45 and 90 is the product of prime factors raised to their respective highest exponent among the numbers 45 and 90.
⇒ LCM of 45, 90 = 2^{1} × 3^{2} × 5^{1} = 90.
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