LCM of 16, 24, 36, and 54
LCM of 16, 24, 36, and 54 is the smallest number among all common multiples of 16, 24, 36, and 54. The first few multiples of 16, 24, 36, and 54 are (16, 32, 48, 64, 80 . . .), (24, 48, 72, 96, 120 . . .), (36, 72, 108, 144, 180 . . .), and (54, 108, 162, 216, 270 . . .) respectively. There are 3 commonly used methods to find LCM of 16, 24, 36, 54  by prime factorization, by division method, and by listing multiples.
1.  LCM of 16, 24, 36, and 54 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 16, 24, 36, and 54?
Answer: LCM of 16, 24, 36, and 54 is 432.
Explanation:
The LCM of four nonzero integers, a(16), b(24), c(36), and d(54), is the smallest positive integer m(432) that is divisible by a(16), b(24), c(36), and d(54) without any remainder.
Methods to Find LCM of 16, 24, 36, and 54
Let's look at the different methods for finding the LCM of 16, 24, 36, and 54.
 By Listing Multiples
 By Prime Factorization Method
 By Division Method
LCM of 16, 24, 36, and 54 by Listing Multiples
To calculate the LCM of 16, 24, 36, 54 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 16 (16, 32, 48, 64, 80 . . .), 24 (24, 48, 72, 96, 120 . . .), 36 (36, 72, 108, 144, 180 . . .), and 54 (54, 108, 162, 216, 270 . . .).
 Step 2: The common multiples from the multiples of 16, 24, 36, and 54 are 432, 864, . . .
 Step 3: The smallest common multiple of 16, 24, 36, and 54 is 432.
∴ The least common multiple of 16, 24, 36, and 54 = 432.
LCM of 16, 24, 36, and 54 by Prime Factorization
Prime factorization of 16, 24, 36, and 54 is (2 × 2 × 2 × 2) = 2^{4}, (2 × 2 × 2 × 3) = 2^{3} × 3^{1}, (2 × 2 × 3 × 3) = 2^{2} × 3^{2}, and (2 × 3 × 3 × 3) = 2^{1} × 3^{3} respectively. LCM of 16, 24, 36, and 54 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{4} × 3^{3} = 432.
Hence, the LCM of 16, 24, 36, and 54 by prime factorization is 432.
LCM of 16, 24, 36, and 54 by Division Method
To calculate the LCM of 16, 24, 36, and 54 by the division method, we will divide the numbers(16, 24, 36, 54) by their prime factors (preferably common). The product of these divisors gives the LCM of 16, 24, 36, and 54.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16, 24, 36, and 54. Write this prime number(2) on the left of the given numbers(16, 24, 36, and 54), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (16, 24, 36, 54) 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 16, 24, 36, and 54 is the product of all prime numbers on the left, i.e. LCM(16, 24, 36, 54) by division method = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432.
ā Also Check:
 LCM of 50 and 70  350
 LCM of 60, 84 and 108  3780
 LCM of 8 and 12  24
 LCM of 2, 3, 4, 5, 6 and 7  420
 LCM of 14 and 24  168
 LCM of 8, 9 and 10  360
 LCM of 9, 12 and 15  180
LCM of 16, 24, 36, and 54 Examples

Example 1: Find the smallest number which when divided by 16, 24, 36, and 54 leaves 4 as the remainder in each case.
Solution:
The smallest number exactly divisible by 16, 24, 36, and 54 = LCM(16, 24, 36, 54) ⇒ Smallest number which leaves 4 as remainder when divided by 16, 24, 36, and 54 = LCM(16, 24, 36, 54) + 4
 16 = 2^{4}
 24 = 2^{3} × 3^{1}
 36 = 2^{2} × 3^{2}
 54 = 2^{1} × 3^{3}
LCM(16, 24, 36, 54) = 2^{4} × 3^{3} = 432
⇒ The required number = 432 + 4 = 436. 
Example 2: Which of the following is the LCM of 16, 24, 36, 54? 36, 5, 432, 24.
Solution:
The value of LCM of 16, 24, 36, and 54 is the smallest common multiple of 16, 24, 36, and 54. The number satisfying the given condition is 432. ∴LCM(16, 24, 36, 54) = 432.

Example 3: Find the smallest number that is divisible by 16, 24, 36, 54 exactly.
Solution:
The value of LCM(16, 24, 36, 54) will be the smallest number that is exactly divisible by 16, 24, 36, and 54.
⇒ Multiples of 16, 24, 36, and 54: Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, . . . ., 384, 400, 416, 432, . . . .
 Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, . . . ., 384, 408, 432, . . . .
 Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, . . . ., 288, 324, 360, 396, 432, . . . .
 Multiples of 54 = 54, 108, 162, 216, 270, 324, 378, 432, 486, 540, . . . ., 216, 270, 324, 378, 432, . . . .
Therefore, the LCM of 16, 24, 36, and 54 is 432.
FAQs on LCM of 16, 24, 36, and 54
What is the LCM of 16, 24, 36, and 54?
The LCM of 16, 24, 36, and 54 is 432. To find the LCM of 16, 24, 36, and 54, we need to find the multiples of 16, 24, 36, and 54 (multiples of 16 = 16, 32, 48, 64 . . . . 432 . . . . ; multiples of 24 = 24, 48, 72, 96 . . . . 432 . . . . ; multiples of 36 = 36, 72, 108, 144 . . . . 432 . . . . ; multiples of 54 = 54, 108, 162, 216 . . . . 432 . . . . ) and choose the smallest multiple that is exactly divisible by 16, 24, 36, and 54, i.e., 432.
What is the Least Perfect Square Divisible by 16, 24, 36, and 54?
The least number divisible by 16, 24, 36, and 54 = LCM(16, 24, 36, 54)
LCM of 16, 24, 36, and 54 = 2 × 2 × 2 × 2 × 3 × 3 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 16, 24, 36, and 54 = LCM(16, 24, 36, 54) × 3 = 1296 [Square root of 1296 = √1296 = ±36]
Therefore, 1296 is the required number.
Which of the following is the LCM of 16, 24, 36, and 54? 11, 432, 52, 5
The value of LCM of 16, 24, 36, 54 is the smallest common multiple of 16, 24, 36, and 54. The number satisfying the given condition is 432.
How to Find the LCM of 16, 24, 36, and 54 by Prime Factorization?
To find the LCM of 16, 24, 36, and 54 using prime factorization, we will find the prime factors, (16 = 2^{4}), (24 = 2^{3} × 3^{1}), (36 = 2^{2} × 3^{2}), and (54 = 2^{1} × 3^{3}). LCM of 16, 24, 36, and 54 is the product of prime factors raised to their respective highest exponent among the numbers 16, 24, 36, and 54.
⇒ LCM of 16, 24, 36, 54 = 2^{4} × 3^{3} = 432.
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