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LCM
Two Numbers Three Numbers Multiple Numbers Prime Factorization Division Listing Multiples Ladder Exponents Venn Diagram Factor Tree
HCF
Two Numbers Three Numbers Multiple Numbers Prime Factorization Listing Ladder Exponents Venn Diagram Division Factor Tree All Factors By Division All Factors By Multiplication

LCM Of Multiple Numbers By Division

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Method
Division Prime Factorization Listing Multiples Ladder Exponents
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Answer: LCM of 18, 24, 54, 60 is 1080
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Step B: Find the LCM Using Division

LCM Method
Calculate LCM
2
18
24
54
60
2
18/
2
24/
2
54/
2
60/
2
9
12
27
30
2
↓
12/
2
↓
30/
2
9
6
27
15
3
↓
6/
2
↓
↓
9
3
27
15
3
9/
3
3/
3
27/
3
15/
3
3
1
9
5
3
3/
3
↓
9/
3
↓
1
1
3
5
5
↓
↓
3/
3
↓
1
1
1
5
↓
↓
↓
5 /
5
1
1
1
1
LCM
=
2
x
2
x
2
x
3
x
3
x
3
x
5
=
1080

Division Help

1. List all the numbers.
2. Take least common prime.
3. Place them on the left.
4. Divide each number.
5. Write quotients below.
6. Repeat until reaching 1.
7. Multiply factors on left side for LCM.

What is Division?

The division method for finding the Least Common Multiple involves dividing the given numbers by common prime number until the remainder is a prime number or one. LCM will be the product obtained by multiplying all divisors and remaining prime numbers.

Solved Examples

Examples

Example 1: Find the LCM of 15 and 20.
Solution:
Divide the given numbers with least common prime number.
Keep dividing until all numbers are fully divided and remainder is 1.
Here, we multiply the all divisors to calculate the LCM.
Therefore, LCM(15, 20) = 60. Example 2: Find the LCM of 15 and 25.
Solution:
Divide the given numbers with least common prime number.
Keep dividing until all numbers are fully divided and remainder is 1.
Here, we multiply the all divisors to calculate the LCM.
Therefore, LCM(15, 25) = 75. Example 3: Find the LCM of 21 and 28.
Solution:
Divide the given numbers with least common prime number.
Keep dividing until all numbers are fully divided and remainder is 1.
Here, we multiply the all divisors to calculate the LCM.
Therefore, LCM(21, 28) = 84.

Exercise

1. LCM(8,12) = 24. 2. LCM(18,27,36) = 108. 3. LCM(15,20,25,30) = 300. 4. LCM(15,25,35) = 525. 5. LCM(10,20,30) = 60. 6. LCM(14,21,28) = 84. 7. LCM(9,12,15) = 180. 8. LCM(16,24,32) = 96. 9. LCM(15,18,24,30) = 360. 10. LCM(20,30,40,50) = 600.

Least Common Multiple (LCM)

What is LCM?

LCM or Least Common Multiple, is the smallest number that is divisible by each of the given numbers without leaving a remainder.
The LCM formula can be expressed as,
LCM Formula:
LCM = (a × b)/ HCF(a,b)
where, a and b = Two terms
HCF(a, b) = Highest common factor of a and b.

How to find LCM?

The Least Common Multiple or LCM can be found using various methods, such as: Prime Factorization MethodDivision MethodListing Multiples MethodLadder MethodExponents MethodVenn Diagram Method

FAQ

What are the steps involved to find LCM?
1. Find common prime factors among the numbers.
2. Divide the numbers by these common primes.
3 .Repeat until the last row reaches 1.
4. Multiply the prime numbers on the left for the LCM.
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