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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
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(Comma Separated)
Steps
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Answer: LCM of 18, 24, 54, 60 is 1080
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Step B: Find the LCM Using Listing Multiples

LCM Method
Calculate LCM
Multiples of 18:
18
36
54
72
90
108
126
144
162
180
198
216
234
252
270
288
306
324
342
360
378
396
414
432
450
468
486
504
522
540
558
576
594
612
630
648
666
684
702
720
738
756
774
792
810
828
846
864
882
900
918
936
954
972
990
1008
1026
1044
1062
1080
1098
1116
Multiples of 24:
24
48
72
96
120
144
168
192
216
240
264
288
312
336
360
384
408
432
456
480
504
528
552
576
600
624
648
672
696
720
744
768
792
816
840
864
888
912
936
960
984
1008
1032
1056
1080
1104
1128
Multiples of 54:
54
108
162
216
270
324
378
432
486
540
594
648
702
756
810
864
918
972
1026
1080
1134
1188
Multiples of 60:
60
120
180
240
300
360
420
480
540
600
660
720
780
840
900
960
1020
1080
1140
1200

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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