LCM of 45 and 72
LCM of 45 and 72 is the smallest number among all common multiples of 45 and 72. The first few multiples of 45 and 72 are (45, 90, 135, 180, 225, 270, 315, . . . ) and (72, 144, 216, 288, 360, 432, 504, . . . ) respectively. There are 3 commonly used methods to find LCM of 45 and 72  by listing multiples, by division method, and by prime factorization.
1.  LCM of 45 and 72 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 45 and 72?
Answer: LCM of 45 and 72 is 360.
Explanation:
The LCM of two nonzero integers, x(45) and y(72), is the smallest positive integer m(360) that is divisible by both x(45) and y(72) without any remainder.
Methods to Find LCM of 45 and 72
Let's look at the different methods for finding the LCM of 45 and 72.
 By Prime Factorization Method
 By Division Method
 By Listing Multiples
LCM of 45 and 72 by Prime Factorization
Prime factorization of 45 and 72 is (3 × 3 × 5) = 3^{2} × 5^{1} and (2 × 2 × 2 × 3 × 3) = 2^{3} × 3^{2} respectively. LCM of 45 and 72 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 3^{2} × 5^{1} = 360.
Hence, the LCM of 45 and 72 by prime factorization is 360.
LCM of 45 and 72 by Division Method
To calculate the LCM of 45 and 72 by the division method, we will divide the numbers(45, 72) by their prime factors (preferably common). The product of these divisors gives the LCM of 45 and 72.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 45 and 72. Write this prime number(2) on the left of the given numbers(45 and 72), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (45, 72) 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 72 is the product of all prime numbers on the left, i.e. LCM(45, 72) by division method = 2 × 2 × 2 × 3 × 3 × 5 = 360.
LCM of 45 and 72 by Listing Multiples
To calculate the LCM of 45 and 72 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 72 (72, 144, 216, 288, 360, 432, 504, . . . . )
 Step 2: The common multiples from the multiples of 45 and 72 are 360, 720, . . .
 Step 3: The smallest common multiple of 45 and 72 is 360.
∴ The least common multiple of 45 and 72 = 360.
☛ Also Check:
 LCM of 45 and 75  225
 LCM of 4, 6 and 9  36
 LCM of 14 and 35  70
 LCM of 6, 7 and 9  126
 LCM of 30 and 35  210
 LCM of 25 and 35  175
 LCM of 3, 9 and 15  45
LCM of 45 and 72 Examples

Example 1: Verify the relationship between GCF and LCM of 45 and 72.
Solution:
The relation between GCF and LCM of 45 and 72 is given as,
LCM(45, 72) × GCF(45, 72) = Product of 45, 72
Prime factorization of 45 and 72 is given as, 45 = (3 × 3 × 5) = 3^{2} × 5^{1} and 72 = (2 × 2 × 2 × 3 × 3) = 2^{3} × 3^{2}
LCM(45, 72) = 360
GCF(45, 72) = 9
LHS = LCM(45, 72) × GCF(45, 72) = 360 × 9 = 3240
RHS = Product of 45, 72 = 45 × 72 = 3240
⇒ LHS = RHS = 3240
Hence, verified. 
Example 2: The product of two numbers is 3240. If their GCD is 9, what is their LCM?
Solution:
Given: GCD = 9
product of numbers = 3240
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 3240/9
Therefore, the LCM is 360.
The probable combination for the given case is LCM(45, 72) = 360. 
Example 3: Find the smallest number that is divisible by 45 and 72 exactly.
Solution:
The smallest number that is divisible by 45 and 72 exactly is their LCM.
⇒ Multiples of 45 and 72: Multiples of 45 = 45, 90, 135, 180, 225, 270, 315, 360, . . . .
 Multiples of 72 = 72, 144, 216, 288, 360, 432, 504, . . . .
Therefore, the LCM of 45 and 72 is 360.
FAQs on LCM of 45 and 72
What is the LCM of 45 and 72?
The LCM of 45 and 72 is 360. To find the LCM of 45 and 72, we need to find the multiples of 45 and 72 (multiples of 45 = 45, 90, 135, 180 . . . . 360; multiples of 72 = 72, 144, 216, 288 . . . . 360) and choose the smallest multiple that is exactly divisible by 45 and 72, i.e., 360.
What is the Relation Between GCF and LCM of 45, 72?
The following equation can be used to express the relation between GCF and LCM of 45 and 72, i.e. GCF × LCM = 45 × 72.
If the LCM of 72 and 45 is 360, Find its GCF.
LCM(72, 45) × GCF(72, 45) = 72 × 45
Since the LCM of 72 and 45 = 360
⇒ 360 × GCF(72, 45) = 3240
Therefore, the greatest common factor (GCF) = 3240/360 = 9.
What are the Methods to Find LCM of 45 and 72?
The commonly used methods to find the LCM of 45 and 72 are:
 Division Method
 Prime Factorization Method
 Listing Multiples
How to Find the LCM of 45 and 72 by Prime Factorization?
To find the LCM of 45 and 72 using prime factorization, we will find the prime factors, (45 = 3 × 3 × 5) and (72 = 2 × 2 × 2 × 3 × 3). LCM of 45 and 72 is the product of prime factors raised to their respective highest exponent among the numbers 45 and 72.
⇒ LCM of 45, 72 = 2^{3} × 3^{2} × 5^{1} = 360.