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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 Listing Multiples

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Multiple Numbers Two Numbers Three Numbers
Method
Listing Multiples Prime Factorization Division Ladder Exponents
Enter Numbers
(Comma Separated)
Steps
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Answer: LCM of 15, 25, 35 is 525
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Step B: Find the LCM Using Listing Multiples

LCM Method
Calculate LCM
Multiples of 15:
15
30
45
60
75
90
105
120
135
150
165
180
195
210
225
240
255
270
285
300
315
330
345
360
375
390
405
420
435
450
465
480
495
510
525
540
555
Multiples of 25:
25
50
75
100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
525
550
575
Multiples of 35:
35
70
105
140
175
210
245
280
315
350
385
420
455
490
525
560
595

Listing Multiples Help

1. List multiples of each number.
2. Identify common multiples.
3. Choose smallest multiple as LCM.

What is Listing Multiples?

The listing multiples method involves finding multiples of each number and identifying common multiples. The smallest common multiple is the LCM of the given numbers.

Solved Examples

Examples

Example 1: Find the LCM of 3 and 5.
Solution:
LCM of 3 and 5: Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...
Smallest common multiple = 15.
Therefore, LCM(3, 5) = 15. Example 2: Find the LCM of 6 and 9.
Solution:
LCM of 6 and 9: Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, ...
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...
Smallest common multiple = 18.
Therefore, LCM(6, 9) = 18. Example 3: Find the LCM of 8 and 12.
Solution:
LCM of 8 and 12: Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ...
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Smallest common multiple = 24.
Therefore, LCM(8, 12) = 24.

Exercise

1. LCM(16,32,48) = 96. 2. LCM(15,25,35) = 525. 3. LCM(15,20,25,30) = 300. 4. LCM(7,11) = 77. 5. LCM(4,6,8) = 24. 6. LCM(5,10,15) = 30. 7. LCM(11,22,33) = 66. 8. LCM(7,14,21) = 42. 9. LCM(10,20,30) = 60. 10. LCM(12,18,24) = 72.

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. Write down the given numbers.
2. List the multiples of each number until you find a common multiple.
3. Identify the least common multiple or LCM from the common multiples.
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