LCM of 16 and 60
LCM of 16 and 60 is the smallest number among all common multiples of 16 and 60. The first few multiples of 16 and 60 are (16, 32, 48, 64, 80, 96, 112, . . . ) and (60, 120, 180, 240, 300, . . . ) respectively. There are 3 commonly used methods to find LCM of 16 and 60  by listing multiples, by prime factorization, and by division method.
1.  LCM of 16 and 60 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 16 and 60?
Answer: LCM of 16 and 60 is 240.
Explanation:
The LCM of two nonzero integers, x(16) and y(60), is the smallest positive integer m(240) that is divisible by both x(16) and y(60) without any remainder.
Methods to Find LCM of 16 and 60
The methods to find the LCM of 16 and 60 are explained below.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 16 and 60 by Prime Factorization
Prime factorization of 16 and 60 is (2 × 2 × 2 × 2) = 2^{4} and (2 × 2 × 3 × 5) = 2^{2} × 3^{1} × 5^{1} respectively. LCM of 16 and 60 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{4} × 3^{1} × 5^{1} = 240.
Hence, the LCM of 16 and 60 by prime factorization is 240.
LCM of 16 and 60 by Listing Multiples
To calculate the LCM of 16 and 60 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, 96, 112, . . . ) and 60 (60, 120, 180, 240, 300, . . . . )
 Step 2: The common multiples from the multiples of 16 and 60 are 240, 480, . . .
 Step 3: The smallest common multiple of 16 and 60 is 240.
∴ The least common multiple of 16 and 60 = 240.
LCM of 16 and 60 by Division Method
To calculate the LCM of 16 and 60 by the division method, we will divide the numbers(16, 60) by their prime factors (preferably common). The product of these divisors gives the LCM of 16 and 60.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 16 and 60. Write this prime number(2) on the left of the given numbers(16 and 60), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (16, 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 16 and 60 is the product of all prime numbers on the left, i.e. LCM(16, 60) by division method = 2 × 2 × 2 × 2 × 3 × 5 = 240.
☛ Also Check:
 LCM of 24, 36 and 72  72
 LCM of 36 and 45  180
 LCM of 25 and 36  900
 LCM of 9 and 33  99
 LCM of 14 and 35  70
 LCM of 12, 16 and 20  240
 LCM of 18 and 30  90
LCM of 16 and 60 Examples

Example 1: Find the smallest number that is divisible by 16 and 60 exactly.
Solution:
The smallest number that is divisible by 16 and 60 exactly is their LCM.
⇒ Multiples of 16 and 60: Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, . . . .
 Multiples of 60 = 60, 120, 180, 240, 300, . . . .
Therefore, the LCM of 16 and 60 is 240.

Example 2: Verify the relationship between GCF and LCM of 16 and 60.
Solution:
The relation between GCF and LCM of 16 and 60 is given as,
LCM(16, 60) × GCF(16, 60) = Product of 16, 60
Prime factorization of 16 and 60 is given as, 16 = (2 × 2 × 2 × 2) = 2^{4} and 60 = (2 × 2 × 3 × 5) = 2^{2} × 3^{1} × 5^{1}
LCM(16, 60) = 240
GCF(16, 60) = 4
LHS = LCM(16, 60) × GCF(16, 60) = 240 × 4 = 960
RHS = Product of 16, 60 = 16 × 60 = 960
⇒ LHS = RHS = 960
Hence, verified. 
Example 3: The GCD and LCM of two numbers are 4 and 240 respectively. If one number is 60, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 60 × y
⇒ y = (GCD × LCM)/60
⇒ y = (4 × 240)/60
⇒ y = 16
Therefore, the other number is 16.
FAQs on LCM of 16 and 60
What is the LCM of 16 and 60?
The LCM of 16 and 60 is 240. To find the LCM (least common multiple) of 16 and 60, we need to find the multiples of 16 and 60 (multiples of 16 = 16, 32, 48, 64 . . . . 240; multiples of 60 = 60, 120, 180, 240) and choose the smallest multiple that is exactly divisible by 16 and 60, i.e., 240.
What is the Least Perfect Square Divisible by 16 and 60?
The least number divisible by 16 and 60 = LCM(16, 60)
LCM of 16 and 60 = 2 × 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 3, 5]
⇒ Least perfect square divisible by each 16 and 60 = LCM(16, 60) × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.
Which of the following is the LCM of 16 and 60? 240, 24, 32, 18
The value of LCM of 16, 60 is the smallest common multiple of 16 and 60. The number satisfying the given condition is 240.
What are the Methods to Find LCM of 16 and 60?
The commonly used methods to find the LCM of 16 and 60 are:
 Prime Factorization Method
 Listing Multiples
 Division Method
If the LCM of 60 and 16 is 240, Find its GCF.
LCM(60, 16) × GCF(60, 16) = 60 × 16
Since the LCM of 60 and 16 = 240
⇒ 240 × GCF(60, 16) = 960
Therefore, the greatest common factor = 960/240 = 4.
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