LCM of 3, 4, 5, and 6
LCM of 3, 4, 5, and 6 is the smallest number among all common multiples of 3, 4, 5, and 6. The first few multiples of 3, 4, 5, and 6 are (3, 6, 9, 12, 15 . . .), (4, 8, 12, 16, 20 . . .), (5, 10, 15, 20, 25 . . .), and (6, 12, 18, 24, 30 . . .) respectively. There are 3 commonly used methods to find LCM of 3, 4, 5, 6  by division method, by prime factorization, and by listing multiples.
1.  LCM of 3, 4, 5, and 6 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 3, 4, 5, and 6?
Answer: LCM of 3, 4, 5, and 6 is 60.
Explanation:
The LCM of four nonzero integers, a(3), b(4), c(5), and d(6), is the smallest positive integer m(60) that is divisible by a(3), b(4), c(5), and d(6) without any remainder.
Methods to Find LCM of 3, 4, 5, and 6
Let's look at the different methods for finding the LCM of 3, 4, 5, and 6.
 By Listing Multiples
 By Prime Factorization Method
 By Division Method
LCM of 3, 4, 5, and 6 by Listing Multiples
To calculate the LCM of 3, 4, 5, 6 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 3 (3, 6, 9, 12, 15 . . .), 4 (4, 8, 12, 16, 20 . . .), 5 (5, 10, 15, 20, 25 . . .), and 6 (6, 12, 18, 24, 30 . . .).
 Step 2: The common multiples from the multiples of 3, 4, 5, and 6 are 60, 120, . . .
 Step 3: The smallest common multiple of 3, 4, 5, and 6 is 60.
∴ The least common multiple of 3, 4, 5, and 6 = 60.
LCM of 3, 4, 5, and 6 by Prime Factorization
Prime factorization of 3, 4, 5, and 6 is (3) = 3^{1}, (2 × 2) = 2^{2}, (5) = 5^{1}, and (2 × 3) = 2^{1} × 3^{1} respectively. LCM of 3, 4, 5, and 6 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{2} × 3^{1} × 5^{1} = 60.
Hence, the LCM of 3, 4, 5, and 6 by prime factorization is 60.
LCM of 3, 4, 5, and 6 by Division Method
To calculate the LCM of 3, 4, 5, and 6 by the division method, we will divide the numbers(3, 4, 5, 6) by their prime factors (preferably common). The product of these divisors gives the LCM of 3, 4, 5, and 6.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3, 4, 5, and 6. Write this prime number(2) on the left of the given numbers(3, 4, 5, and 6), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (3, 4, 5, 6) 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 3, 4, 5, and 6 is the product of all prime numbers on the left, i.e. LCM(3, 4, 5, 6) by division method = 2 × 2 × 3 × 5 = 60.
ā Also Check:
 LCM of 30 and 48  240
 LCM of 3, 5 and 8  120
 LCM of 3 and 6  6
 LCM of 8 and 22  88
 LCM of 63 and 81  567
 LCM of 36 and 64  576
 LCM of 30 and 45  90
LCM of 3, 4, 5, and 6 Examples

Example 1: Which of the following is the LCM of 3, 4, 5, 6? 120, 60, 15, 20.
Solution:
The value of LCM of 3, 4, 5, and 6 is the smallest common multiple of 3, 4, 5, and 6. The number satisfying the given condition is 60. ∴LCM(3, 4, 5, 6) = 60.

Example 2: Find the smallest number which when divided by 3, 4, 5, and 6 leaves 2 as the remainder in each case.
Solution:
The smallest number exactly divisible by 3, 4, 5, and 6 = LCM(3, 4, 5, 6) ⇒ Smallest number which leaves 2 as remainder when divided by 3, 4, 5, and 6 = LCM(3, 4, 5, 6) + 2
 3 = 3^{1}
 4 = 2^{2}
 5 = 5^{1}
 6 = 2^{1} × 3^{1}
LCM(3, 4, 5, 6) = 2^{2} × 3^{1} × 5^{1} = 60
⇒ The required number = 60 + 2 = 62. 
Example 3: Find the smallest number that is divisible by 3, 4, 5, 6 exactly.
Solution:
The value of LCM(3, 4, 5, 6) will be the smallest number that is exactly divisible by 3, 4, 5, and 6.
⇒ Multiples of 3, 4, 5, and 6: Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 48, 51, 54, 57, 60, . . . .
 Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . ., 52, 56, 60, . . . .
 Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 45, 50, 55, 60, . . . .
 Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . ., 42, 48, 54, 60, . . . .
Therefore, the LCM of 3, 4, 5, and 6 is 60.
FAQs on LCM of 3, 4, 5, and 6
What is the LCM of 3, 4, 5, and 6?
The LCM of 3, 4, 5, and 6 is 60. To find the LCM (least common multiple) of 3, 4, 5, and 6, we need to find the multiples of 3, 4, 5, and 6 (multiples of 3 = 3, 6, 9, 12 . . . . 60 . . . . ; multiples of 4 = 4, 8, 12, 16 . . . . 60 . . . . ; multiples of 5 = 5, 10, 15, 20 . . . . 60 . . . . ; multiples of 6 = 6, 12, 18, 24 . . . . 60 . . . . ) and choose the smallest multiple that is exactly divisible by 3, 4, 5, and 6, i.e., 60.
What is the Least Perfect Square Divisible by 3, 4, 5, and 6?
The least number divisible by 3, 4, 5, and 6 = LCM(3, 4, 5, 6)
LCM of 3, 4, 5, and 6 = 2 × 2 × 3 × 5 [Incomplete pair(s): 3, 5]
⇒ Least perfect square divisible by each 3, 4, 5, and 6 = LCM(3, 4, 5, 6) × 3 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.
What are the Methods to Find LCM of 3, 4, 5, 6?
The commonly used methods to find the LCM of 3, 4, 5, 6 are:
 Division Method
 Listing Multiples
 Prime Factorization Method
Which of the following is the LCM of 3, 4, 5, and 6? 60, 3, 52, 12
The value of LCM of 3, 4, 5, 6 is the smallest common multiple of 3, 4, 5, and 6. The number satisfying the given condition is 60.
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