LCM of 54 and 60
LCM of 54 and 60 is the smallest number among all common multiples of 54 and 60. The first few multiples of 54 and 60 are (54, 108, 162, 216, 270, 324, . . . ) and (60, 120, 180, 240, . . . ) respectively. There are 3 commonly used methods to find LCM of 54 and 60  by prime factorization, by division method, and by listing multiples.
1.  LCM of 54 and 60 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 54 and 60?
Answer: LCM of 54 and 60 is 540.
Explanation:
The LCM of two nonzero integers, x(54) and y(60), is the smallest positive integer m(540) that is divisible by both x(54) and y(60) without any remainder.
Methods to Find LCM of 54 and 60
Let's look at the different methods for finding the LCM of 54 and 60.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 54 and 60 by Prime Factorization
Prime factorization of 54 and 60 is (2 × 3 × 3 × 3) = 2^{1} × 3^{3} and (2 × 2 × 3 × 5) = 2^{2} × 3^{1} × 5^{1} respectively. LCM of 54 and 60 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{3} × 5^{1} = 540.
Hence, the LCM of 54 and 60 by prime factorization is 540.
LCM of 54 and 60 by Listing Multiples
To calculate the LCM of 54 and 60 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 54 (54, 108, 162, 216, 270, 324, . . . ) and 60 (60, 120, 180, 240, . . . . )
 Step 2: The common multiples from the multiples of 54 and 60 are 540, 1080, . . .
 Step 3: The smallest common multiple of 54 and 60 is 540.
∴ The least common multiple of 54 and 60 = 540.
LCM of 54 and 60 by Division Method
To calculate the LCM of 54 and 60 by the division method, we will divide the numbers(54, 60) by their prime factors (preferably common). The product of these divisors gives the LCM of 54 and 60.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 54 and 60. Write this prime number(2) on the left of the given numbers(54 and 60), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (54, 60) 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 54 and 60 is the product of all prime numbers on the left, i.e. LCM(54, 60) by division method = 2 × 2 × 3 × 3 × 3 × 5 = 540.
☛ Also Check:
 LCM of 4 and 10  20
 LCM of 36 and 72  72
 LCM of 56 and 70  280
 LCM of 40, 48 and 45  720
 LCM of 8, 9 and 12  72
 LCM of 4 and 20  20
 LCM of 30, 36 and 40  360
LCM of 54 and 60 Examples

Example 1: The product of two numbers is 3240. If their GCD is 6, what is their LCM?
Solution:
Given: GCD = 6
product of numbers = 3240
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 3240/6
Therefore, the LCM is 540.
The probable combination for the given case is LCM(54, 60) = 540. 
Example 2: The GCD and LCM of two numbers are 6 and 540 respectively. If one number is 54, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 54 × z
⇒ z = (GCD × LCM)/54
⇒ z = (6 × 540)/54
⇒ z = 60
Therefore, the other number is 60. 
Example 3: Verify the relationship between GCF and LCM of 54 and 60.
Solution:
The relation between GCF and LCM of 54 and 60 is given as,
LCM(54, 60) × GCF(54, 60) = Product of 54, 60
Prime factorization of 54 and 60 is given as, 54 = (2 × 3 × 3 × 3) = 2^{1} × 3^{3} and 60 = (2 × 2 × 3 × 5) = 2^{2} × 3^{1} × 5^{1}
LCM(54, 60) = 540
GCF(54, 60) = 6
LHS = LCM(54, 60) × GCF(54, 60) = 540 × 6 = 3240
RHS = Product of 54, 60 = 54 × 60 = 3240
⇒ LHS = RHS = 3240
Hence, verified.
FAQs on LCM of 54 and 60
What is the LCM of 54 and 60?
The LCM of 54 and 60 is 540. To find the least common multiple (LCM) of 54 and 60, we need to find the multiples of 54 and 60 (multiples of 54 = 54, 108, 162, 216 . . . . 540; multiples of 60 = 60, 120, 180, 240 . . . . 540) and choose the smallest multiple that is exactly divisible by 54 and 60, i.e., 540.
What are the Methods to Find LCM of 54 and 60?
The commonly used methods to find the LCM of 54 and 60 are:
 Listing Multiples
 Division Method
 Prime Factorization Method
What is the Least Perfect Square Divisible by 54 and 60?
The least number divisible by 54 and 60 = LCM(54, 60)
LCM of 54 and 60 = 2 × 2 × 3 × 3 × 3 × 5 [Incomplete pair(s): 3, 5]
⇒ Least perfect square divisible by each 54 and 60 = LCM(54, 60) × 3 × 5 = 8100 [Square root of 8100 = √8100 = ±90]
Therefore, 8100 is the required number.
If the LCM of 60 and 54 is 540, Find its GCF.
LCM(60, 54) × GCF(60, 54) = 60 × 54
Since the LCM of 60 and 54 = 540
⇒ 540 × GCF(60, 54) = 3240
Therefore, the GCF (greatest common factor) = 3240/540 = 6.
How to Find the LCM of 54 and 60 by Prime Factorization?
To find the LCM of 54 and 60 using prime factorization, we will find the prime factors, (54 = 2 × 3 × 3 × 3) and (60 = 2 × 2 × 3 × 5). LCM of 54 and 60 is the product of prime factors raised to their respective highest exponent among the numbers 54 and 60.
⇒ LCM of 54, 60 = 2^{2} × 3^{3} × 5^{1} = 540.
visual curriculum