LCM of 8, 15, and 20
LCM of 8, 15, and 20 is the smallest number among all common multiples of 8, 15, and 20. The first few multiples of 8, 15, and 20 are (8, 16, 24, 32, 40 . . .), (15, 30, 45, 60, 75 . . .), and (20, 40, 60, 80, 100 . . .) respectively. There are 3 commonly used methods to find LCM of 8, 15, 20  by prime factorization, by listing multiples, and by division method.
1.  LCM of 8, 15, and 20 
2.  List of Methods 
3.  Solved Examples 
4.  FAQs 
What is the LCM of 8, 15, and 20?
Answer: LCM of 8, 15, and 20 is 120.
Explanation:
The LCM of three nonzero integers, a(8), b(15), and c(20), is the smallest positive integer m(120) that is divisible by a(8), b(15), and c(20) without any remainder.
Methods to Find LCM of 8, 15, and 20
Let's look at the different methods for finding the LCM of 8, 15, and 20.
 By Prime Factorization Method
 By Listing Multiples
 By Division Method
LCM of 8, 15, and 20 by Prime Factorization
Prime factorization of 8, 15, and 20 is (2 × 2 × 2) = 2^{3}, (3 × 5) = 3^{1} × 5^{1}, and (2 × 2 × 5) = 2^{2} × 5^{1} respectively. LCM of 8, 15, and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2^{3} × 3^{1} × 5^{1} = 120.
Hence, the LCM of 8, 15, and 20 by prime factorization is 120.
LCM of 8, 15, and 20 by Listing Multiples
To calculate the LCM of 8, 15, 20 by listing out the common multiples, we can follow the given below steps:
 Step 1: List a few multiples of 8 (8, 16, 24, 32, 40 . . .), 15 (15, 30, 45, 60, 75 . . .), and 20 (20, 40, 60, 80, 100 . . .).
 Step 2: The common multiples from the multiples of 8, 15, and 20 are 120, 240, . . .
 Step 3: The smallest common multiple of 8, 15, and 20 is 120.
∴ The least common multiple of 8, 15, and 20 = 120.
LCM of 8, 15, and 20 by Division Method
To calculate the LCM of 8, 15, and 20 by the division method, we will divide the numbers(8, 15, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 8, 15, and 20.
 Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8, 15, and 20. Write this prime number(2) on the left of the given numbers(8, 15, and 20), separated as per the ladder arrangement.
 Step 2: If any of the given numbers (8, 15, 20) 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 8, 15, and 20 is the product of all prime numbers on the left, i.e. LCM(8, 15, 20) by division method = 2 × 2 × 2 × 3 × 5 = 120.
ā Also Check:
 LCM of 15 and 30  30
 LCM of 18, 24 and 36  72
 LCM of 54 and 72  216
 LCM of 28 and 42  84
 LCM of 16 and 48  48
 LCM of 14 and 56  56
 LCM of 4 and 5  20
LCM of 8, 15, and 20 Examples

Example 1: Verify the relationship between the GCD and LCM of 8, 15, and 20.
Solution:
The relation between GCD and LCM of 8, 15, and 20 is given as,
LCM(8, 15, 20) = [(8 × 15 × 20) × GCD(8, 15, 20)]/[GCD(8, 15) × GCD(15, 20) × GCD(8, 20)]
⇒ Prime factorization of 8, 15 and 20: 8 = 2^{3}
 15 = 3^{1} × 5^{1}
 20 = 2^{2} × 5^{1}
∴ GCD of (8, 15), (15, 20), (8, 20) and (8, 15, 20) = 1, 5, 4 and 1 respectively.
Now, LHS = LCM(8, 15, 20) = 120.
And, RHS = [(8 × 15 × 20) × GCD(8, 15, 20)]/[GCD(8, 15) × GCD(15, 20) × GCD(8, 20)] = [(2400) × 1]/[1 × 5 × 4] = 120
LHS = RHS = 120.
Hence verified. 
Example 2: Calculate the LCM of 8, 15, and 20 using the GCD of the given numbers.
Solution:
Prime factorization of 8, 15, 20:
 8 = 2^{3}
 15 = 3^{1} × 5^{1}
 20 = 2^{2} × 5^{1}
Therefore, GCD(8, 15) = 1, GCD(15, 20) = 5, GCD(8, 20) = 4, GCD(8, 15, 20) = 1
We know,
LCM(8, 15, 20) = [(8 × 15 × 20) × GCD(8, 15, 20)]/[GCD(8, 15) × GCD(15, 20) × GCD(8, 20)]
LCM(8, 15, 20) = (2400 × 1)/(1 × 5 × 4) = 120
⇒LCM(8, 15, 20) = 120 
Example 3: Find the smallest number that is divisible by 8, 15, 20 exactly.
Solution:
The smallest number that is divisible by 8, 15, and 20 exactly is their LCM.
⇒ Multiples of 8, 15, and 20: Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, . . . .
 Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, . . . .
 Multiples of 20 = 20, 40, 60, 80, 100, 120, . . . .
Therefore, the LCM of 8, 15, and 20 is 120.
FAQs on LCM of 8, 15, and 20
What is the LCM of 8, 15, and 20?
The LCM of 8, 15, and 20 is 120. To find the LCM of 8, 15, and 20, we need to find the multiples of 8, 15, and 20 (multiples of 8 = 8, 16, 24, 32 . . . . 120 . . . . ; multiples of 15 = 15, 30, 45, 60 . . . . 120 . . . . ; multiples of 20 = 20, 40, 60, 80, 120 . . . .) and choose the smallest multiple that is exactly divisible by 8, 15, and 20, i.e., 120.
Which of the following is the LCM of 8, 15, and 20? 120, 25, 20, 50
The value of LCM of 8, 15, 20 is the smallest common multiple of 8, 15, and 20. The number satisfying the given condition is 120.
What is the Relation Between GCF and LCM of 8, 15, 20?
The following equation can be used to express the relation between GCF and LCM of 8, 15, 20, i.e. LCM(8, 15, 20) = [(8 × 15 × 20) × GCF(8, 15, 20)]/[GCF(8, 15) × GCF(15, 20) × GCF(8, 20)].
How to Find the LCM of 8, 15, and 20 by Prime Factorization?
To find the LCM of 8, 15, and 20 using prime factorization, we will find the prime factors, (8 = 2^{3}), (15 = 3^{1} × 5^{1}), and (20 = 2^{2} × 5^{1}). LCM of 8, 15, and 20 is the product of prime factors raised to their respective highest exponent among the numbers 8, 15, and 20.
⇒ LCM of 8, 15, 20 = 2^{3} × 3^{1} × 5^{1} = 120.