LCM of 186 and 403
LCM of 186 and 403 is the smallest number among all common multiples of 186 and 403. The first few multiples of 186 and 403 are (186, 372, 558, 744, 930, . . . ) and (403, 806, 1209, 1612, 2015, . . . ) respectively. There are 3 commonly used methods to find LCM of 186 and 403  by division method, by prime factorization, and by listing multiples.
1.  LCM of 186 and 403 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 186 and 403?
Answer: LCM of 186 and 403 is 2418.
Explanation:
The LCM of two nonzero integers, x(186) and y(403), is the smallest positive integer m(2418) that is divisible by both x(186) and y(403) without any remainder.
Methods to Find LCM of 186 and 403
Let's look at the different methods for finding the LCM of 186 and 403.
 By Division Method
 By Prime Factorization Method
 By Listing Multiples
LCM of 186 and 403 by Division Method
To calculate the LCM of 186 and 403 by the division method, we will divide the numbers(186, 403) by their prime factors (preferably common). The product of these divisors gives the LCM of 186 and 403.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 186 and 403. Write this prime number(2) on the left of the given numbers(186 and 403), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (186, 403) 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 186 and 403 is the product of all prime numbers on the left, i.e. LCM(186, 403) by division method = 2 × 3 × 13 × 31 = 2418.
LCM of 186 and 403 by Prime Factorization
Prime factorization of 186 and 403 is (2 × 3 × 31) = 2^{1} × 3^{1} × 31^{1} and (13 × 31) = 13^{1} × 31^{1} respectively. LCM of 186 and 403 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{1} × 3^{1} × 13^{1} × 31^{1} = 2418.
Hence, the LCM of 186 and 403 by prime factorization is 2418.
LCM of 186 and 403 by Listing Multiples
To calculate the LCM of 186 and 403 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 186 (186, 372, 558, 744, 930, . . . ) and 403 (403, 806, 1209, 1612, 2015, . . . . )
 Step 2: The common multiples from the multiples of 186 and 403 are 2418, 4836, . . .
 Step 3: The smallest common multiple of 186 and 403 is 2418.
∴ The least common multiple of 186 and 403 = 2418.
☛ Also Check:
 LCM of 15 and 60  60
 LCM of 16 and 64  64
 LCM of 8 and 32  32
 LCM of 125 and 175  875
 LCM of 2 and 5  10
 LCM of 36 and 90  180
 LCM of 12, 45 and 75  900
LCM of 186 and 403 Examples

Example 1: Verify the relationship between GCF and LCM of 186 and 403.
Solution:
The relation between GCF and LCM of 186 and 403 is given as,
LCM(186, 403) × GCF(186, 403) = Product of 186, 403
Prime factorization of 186 and 403 is given as, 186 = (2 × 3 × 31) = 2^{1} × 3^{1} × 31^{1} and 403 = (13 × 31) = 13^{1} × 31^{1}
LCM(186, 403) = 2418
GCF(186, 403) = 31
LHS = LCM(186, 403) × GCF(186, 403) = 2418 × 31 = 74958
RHS = Product of 186, 403 = 186 × 403 = 74958
⇒ LHS = RHS = 74958
Hence, verified. 
Example 2: Find the smallest number that is divisible by 186 and 403 exactly.
Solution:
The smallest number that is divisible by 186 and 403 exactly is their LCM.
⇒ Multiples of 186 and 403: Multiples of 186 = 186, 372, 558, 744, 930, 1116, 1302, 1488, 1674, 1860, 2046, 2232, 2418, . . . .
 Multiples of 403 = 403, 806, 1209, 1612, 2015, 2418, . . . .
Therefore, the LCM of 186 and 403 is 2418.

Example 3: The GCD and LCM of two numbers are 31 and 2418 respectively. If one number is 186, find the other number.
Solution:
Let the other number be z.
∵ GCD × LCM = 186 × z
⇒ z = (GCD × LCM)/186
⇒ z = (31 × 2418)/186
⇒ z = 403
Therefore, the other number is 403.
FAQs on LCM of 186 and 403
What is the LCM of 186 and 403?
The LCM of 186 and 403 is 2418. To find the least common multiple (LCM) of 186 and 403, we need to find the multiples of 186 and 403 (multiples of 186 = 186, 372, 558, 744 . . . . 2418; multiples of 403 = 403, 806, 1209, 1612 . . . . 2418) and choose the smallest multiple that is exactly divisible by 186 and 403, i.e., 2418.
Which of the following is the LCM of 186 and 403? 3, 50, 45, 2418
The value of LCM of 186, 403 is the smallest common multiple of 186 and 403. The number satisfying the given condition is 2418.
If the LCM of 403 and 186 is 2418, Find its GCF.
LCM(403, 186) × GCF(403, 186) = 403 × 186
Since the LCM of 403 and 186 = 2418
⇒ 2418 × GCF(403, 186) = 74958
Therefore, the greatest common factor = 74958/2418 = 31.
What are the Methods to Find LCM of 186 and 403?
The commonly used methods to find the LCM of 186 and 403 are:
 Listing Multiples
 Division Method
 Prime Factorization Method
How to Find the LCM of 186 and 403 by Prime Factorization?
To find the LCM of 186 and 403 using prime factorization, we will find the prime factors, (186 = 2 × 3 × 31) and (403 = 13 × 31). LCM of 186 and 403 is the product of prime factors raised to their respective highest exponent among the numbers 186 and 403.
⇒ LCM of 186, 403 = 2^{1} × 3^{1} × 13^{1} × 31^{1} = 2418.
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