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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 Three Numbers By Listing Multiples

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Three Numbers Two Numbers Multiple Numbers
Method
Listing Multiples Prime Factorization Venn Diagram Division Ladder Exponents
Enter Numbers
(Comma Separated)
Steps
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Answer: LCM of 5, 11, 13 is 715
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Step B: Find the LCM Using Listing Multiples

LCM Method
Calculate LCM
Multiples of 5:
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
130
135
140
145
150
155
160
165
170
175
180
185
190
195
200
205
210
215
220
225
230
235
240
245
250
255
260
265
270
275
280
285
290
295
300
305
310
315
320
325
330
335
340
345
350
355
360
365
370
375
380
385
390
395
400
405
410
415
420
425
430
435
440
445
450
455
460
465
470
475
480
485
490
495
500
505
510
515
520
525
530
535
540
545
550
555
560
565
570
575
580
585
590
595
600
605
610
615
620
625
630
635
640
645
650
655
660
665
670
675
680
685
690
695
700
705
710
715
720
725
Multiples of 11:
11
22
33
44
55
66
77
88
99
110
121
132
143
154
165
176
187
198
209
220
231
242
253
264
275
286
297
308
319
330
341
352
363
374
385
396
407
418
429
440
451
462
473
484
495
506
517
528
539
550
561
572
583
594
605
616
627
638
649
660
671
682
693
704
715
726
737
Multiples of 13:
13
26
39
52
65
78
91
104
117
130
143
156
169
182
195
208
221
234
247
260
273
286
299
312
325
338
351
364
377
390
403
416
429
442
455
468
481
494
507
520
533
546
559
572
585
598
611
624
637
650
663
676
689
702
715
728
741

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 2, 5 and 8.
Solution:
LCM of 2 and 5: Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ...
Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ...
Smallest common multiple is 40.
Therefore, LCM(2, 5, 8) = 40. Example 2: Find the LCM of 12, 16 and 20.
Solution:
LCM of 12 and 16: Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, ...
Multiples of 20 = 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, ...
Smallest common multiple is 240.
Therefore, LCM(12, 16, 20) = 240. Example 3: Find the LCM of 8, 10 and 12.
Solution:
LCM of 8 and 10: Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ...
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Smallest common multiple is 120.
Therefore, LCM(8, 10, 12) = 120.

Exercise

1. LCM(3,5,7) = 105. 2. LCM(8,10,12) = 120. 3. LCM(12,16,20) = 240. 4. LCM(18,24,10) = 360. 5. LCM(30,40,25) = 600. 6. LCM(4,5,8) = 40. 7. LCM(9,12,16) = 144. 8. LCM(6,8,16) = 48. 9. LCM(5,11,13) = 715. 10. LCM(30,45,150) = 450.

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. Input three numbers into the calculator.
2. List the multiples of each number.
3. Identify the smallest common multiple as the LCM.
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