LCM of 16 and 40
LCM of 16 and 40 is the smallest number among all common multiples of 16 and 40. The first few multiples of 16 and 40 are (16, 32, 48, 64, . . . ) and (40, 80, 120, 160, 200, 240, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 40  by listing multiples, by prime factorization, and by division method.
1.  LCM of 16 and 40 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 16 and 40?
Answer: LCM of 16 and 40 is 80.
Explanation:
The LCM of two nonzero integers, x(16) and y(40), is the smallest positive integer m(80) that is divisible by both x(16) and y(40) without any remainder.
Methods to Find LCM of 16 and 40
Let's look at the different methods for finding the LCM of 16 and 40.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 16 and 40 by Division Method
To calculate the LCM of 16 and 40 by the division method, we will divide the numbers(16, 40) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 40.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 40. Write this prime number(2) on the left of the given numbers(16 and 40), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (16, 40) 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 and 40 is the product of all prime numbers on the left, i.e. LCM(16, 40) by division method = 2 × 2 × 2 × 2 × 5 = 80.
LCM of 16 and 40 by Prime Factorization
Prime factorization of 16 and 40 is (2 × 2 × 2 × 2) = 2^{4} and (2 × 2 × 2 × 5) = 2^{3} × 5^{1} respectively. LCM of 16 and 40 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{4} × 5^{1} = 80.
Hence, the LCM of 16 and 40 by prime factorization is 80.
LCM of 16 and 40 by Listing Multiples
To calculate the LCM of 16 and 40 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, . . . ) and 40 (40, 80, 120, 160, 200, 240, . . . . )
 Step 2: The common multiples from the multiples of 16 and 40 are 80, 160, . . .
 Step 3: The smallest common multiple of 16 and 40 is 80.
∴ The least common multiple of 16 and 40 = 80.
☛ Also Check:
 LCM of 32 and 36  288
 LCM of 21, 28, 36 and 45  1260
 LCM of 5 and 24  120
 LCM of 25 and 50  50
 LCM of 12 and 30  60
 LCM of 20 and 50  100
 LCM of 26 and 39  78
LCM of 16 and 40 Examples

Example 1: Verify the relationship between GCF and LCM of 16 and 40.
Solution:
The relation between GCF and LCM of 16 and 40 is given as,
LCM(16, 40) × GCF(16, 40) = Product of 16, 40
Prime factorization of 16 and 40 is given as, 16 = (2 × 2 × 2 × 2) = 2^{4} and 40 = (2 × 2 × 2 × 5) = 2^{3} × 5^{1}
LCM(16, 40) = 80
GCF(16, 40) = 8
LHS = LCM(16, 40) × GCF(16, 40) = 80 × 8 = 640
RHS = Product of 16, 40 = 16 × 40 = 640
⇒ LHS = RHS = 640
Hence, verified. 
Example 2: The GCD and LCM of two numbers are 8 and 80 respectively. If one number is 16, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 16 × p
⇒ p = (GCD × LCM)/16
⇒ p = (8 × 80)/16
⇒ p = 40
Therefore, the other number is 40. 
Example 3: Find the smallest number that is divisible by 16 and 40 exactly.
Solution:
The smallest number that is divisible by 16 and 40 exactly is their LCM.
⇒ Multiples of 16 and 40: Multiples of 16 = 16, 32, 48, 64, 80, . . . .
 Multiples of 40 = 40, 80, 120, 160, 200, . . . .
Therefore, the LCM of 16 and 40 is 80.
FAQs on LCM of 16 and 40
What is the LCM of 16 and 40?
The LCM of 16 and 40 is 80. To find the least common multiple of 16 and 40, we need to find the multiples of 16 and 40 (multiples of 16 = 16, 32, 48, 64 . . . . 80; multiples of 40 = 40, 80, 120, 160) and choose the smallest multiple that is exactly divisible by 16 and 40, i.e., 80.
If the LCM of 40 and 16 is 80, Find its GCF.
LCM(40, 16) × GCF(40, 16) = 40 × 16
Since the LCM of 40 and 16 = 80
⇒ 80 × GCF(40, 16) = 640
Therefore, the greatest common factor (GCF) = 640/80 = 8.
What is the Least Perfect Square Divisible by 16 and 40?
The least number divisible by 16 and 40 = LCM(16, 40)
LCM of 16 and 40 = 2 × 2 × 2 × 2 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 16 and 40 = LCM(16, 40) × 5 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.
What is the Relation Between GCF and LCM of 16, 40?
The following equation can be used to express the relation between GCF and LCM of 16 and 40, i.e. GCF × LCM = 16 × 40.
How to Find the LCM of 16 and 40 by Prime Factorization?
To find the LCM of 16 and 40 using prime factorization, we will find the prime factors, (16 = 2 × 2 × 2 × 2) and (40 = 2 × 2 × 2 × 5). LCM of 16 and 40 is the product of prime factors raised to their respective highest exponent among the numbers 16 and 40.
⇒ LCM of 16, 40 = 2^{4} × 5^{1} = 80.
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