Least Common Factor Calculator

Enter the value that you want to calculate LCM..

First number:
Second number:
Greatest common factor (gcf):
Least common multiple (lcm):

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Table of least common multiples (to 32)

X 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
2 2 2 6 4 10 6 14 8 18 10 22 12 26 14 30 16 34 18 38 20 42 22 46 24 50 26 54 28 58 30 62 32
3 3 6 3 12 15 6 21 24 9 30 33 12 39 42 15 48 51 18 57 60 21 66 69 24 75 78 27 84 87 30 93 96
4 4 4 12 4 20 12 28 24 36 20 44 12 52 28 60 16 68 36 76 20 84 44 92 24 100 52 108 28 116 60 124 32
5 5 10 15 20 5 30 35 40 45 10 55 60 65 70 15 80 85 90 95 20 105 110 115 120 25 130 135 140 145 30 155 160
6 6 6 6 12 30 6 42 24 18 30 66 12 78 42 30 48 102 18 114 60 42 66 138 24 150 78 54 84 174 30 186 96
7 7 14 21 28 35 42 7 56 63 70 77 84 91 14 105 112 119 126 133 140 21 154 161 168 175 182 189 28 203 210 217 224
8 8 8 24 8 40 24 56 64 73 40 88 24 104 56 120 16 136 72 152 40 168 88 184 24 200 104 216 56 232 120 248 32
9 9 18 9 36 45 18 63 72 9 90 99 36 117 126 45 144 153 18 171 180 63 198 207 72 225 234 27 252 261 90 279 288
10 10 10 30 20 10 30 70 40 90 10 110 60 130 70 30 80 170 90 190 20 210 110 230 120 50 130 270 140 290 30 310 160
11 11 22 33 44 55 66 77 88 99 110 11 132 143 154 165 176 187 198 209 220 231 22 253 264 275 286 297 308 319 330 341 352
12 12 12 12 12 60 12 84 24 36 60 132 12 156 84 60 48 204 36 228 60 84 132 276 24 300 156 108 84 348 60 372 96
13 13 26 39 52 65 78 91 104 117 130 143 156 13 182 195 208 221 234 247 260 273 286 299 312 325 26 351 364 377 390 403 416
14 14 14 42 28 70 42 14 56 126 70 154 84 182 14 210 112 238 126 266 140 42 154 322 168 350 182 378 28 406 210 434 224
15 15 30 15 60 15 30 105 120 45 30 165 60 195 210 15 240 255 90 285 60 105 330 345 120 75 390 135 420 435 30 465 480
16 16 16 48 16 80 48 112 16 144 80 176 48 208 112 240 16 272 144 304 80 336 176 368 48 400 208 432 112 464 240 496 32
17 17 34 51 68 85 102 119 136 153 170 187 204 221 238 255 272 17 306 323 340 357 374 391 408 425 442 459 476 493 510 527 544
18 18 18 18 36 90 18 126 72 18 90 198 36 234 126 90 144 306 18 342 180 126 198 414 72 450 234 54 252 522 90 558 288
19 19 38 57 76 95 114 133 152 171 190 209 228 247 266 285 304 323 342 19 380 399 418 437 456 475 494 513 532 551 570 589 608
20 20 20 60 20 20 60 140 40 180 20 220 60 260 140 60 80 340 180 380 20 420 220 460 120 100 260 540 140 580 60 620 160
21 21 42 21 84 105 42 21 168 63 210 231 84 273 42 105 336 357 126 399 420 21 462 483 168 525 546 189 84 609 210 651 672
22 22 22 66 44 110 66 154 88 198 110 22 132 286 154 330 176 374 198 418 220 462 22 506 264 550 286 594 308 638 330 682 352
23 23 46 69 92 115 138 161 184 207 230 253 276 299 322 345 368 391 414 437 460 483 506 23 552 575 598 621 644 667 690 713 736
24 24 24 24 24 120 24 168 24 72 120 264 24 312 168 120 48 408 72 456 120 168 264 552 24 600 312 216 168 696 120 744 96
25 25 50 75 100 25 150 175 200 225 50 275 300 325 350 75 400 425 450 475 100 525 550 575 600 25 650 675 700 725 150 775 800
26 26 26 78 52 130 78 182 104 234 130 286 156 26 182 390 208 442 234 494 260 546 286 598 312 650 26 702 364 754 390 806 416
27 27 54 27 108 135 54 189 216 27 270 297 108 351 378 135 432 459 54 513 540 189 594 621 216 675 702 27 756 783 270 837 864
28 28 28 84 28 140 84 28 56 252 140 308 84 364 28 420 112 476 252 532 140 84 308 644 168 700 364 756 28 812 420 868 224
29 29 58 87 116 145 174 203 232 261 290 319 348 377 406 435 464 493 522 551 580 609 638 667 696 725 754 783 812 29 870 899 928
30 30 30 30 60 30 30 210 120 90 30 330 60 390 210 30 240 510 90 570 60 210 330 690 120 150 390 270 420 870 30 930 480
31 31 62 93 124 155 186 217 248 279 310 341 372 403 434 465 496 527 558 589 620 651 682 713 744 775 806 837 868 899 930 31 992
32 32 32 96 32 160 96 224 32 288 160 352 96 416 224 480 32 544 288 608 160 672 352 736 96 800 416 864 224 928 480 992 32

LCM Calculator: Simplifying Math One Number at a Time

Our LCM Calculator is a powerful tool designed to find the least common multiple of two or more numbers, streamlining calculations for students, educators, and professionals alike. This calculator not only provides the LCM but also the greatest common factor (GCF), enhancing your mathematical toolkit.

Understanding LCM

The Least Common Multiple (LCM) of two integers is the smallest integer that is a multiple of both numbers. It's crucial in solving problems involving fractions, ratios, and when participating in operations requiring common denominators.

How It Works

  1. Input Numbers: Enter two or more numbers to find their LCM.
  2. Calculation: The calculator uses efficient algorithms to compute the LCM alongside the GCF, providing a comprehensive mathematical analysis.

Formulas

LCM Calculation: The LCM of two numbers \(a\) and \(b\) can be found using the formula: \( \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCF}(a, b)} \), where GCF is the greatest common factor.

GCF Calculation: The GCF of \(a\) and \(b\) is the largest positive integer that divides both \(a\) and \(b\) without a remainder.

Practical Uses

LCM is widely used in adding, subtracting, and comparing fractions, scheduling events, and in solving various algebraic problems. It's a fundamental concept in number theory and plays a vital role in computational mathematics.

Frequently Asked Questions

How do you find the least common multiple?
The LCM is found by determining the greatest common divisor (GCD) of the numbers and using the relationship between GCD and LCM.
What is the LCM of 5 and 3?
The LCM of 5 and 3 is 15, as 15 is the smallest number that both 5 and 3 can divide into without leaving a remainder.
What is the LCD of 9 and 12?
The least common denominator (LCD), similar to LCM for fractions, of 9 and 12 is 36, which is the LCM of the denominators.
How to multiply a fraction?
To multiply fractions, multiply the numerators together and the denominators together. The LCM can be used to simplify the fractions if needed.
What is the LCM of 5?
The LCM of a single number like 5 is itself, which is 5, as it's the smallest multiple of 5.
What is the LCM of 5 and 8?
The LCM of 5 and 8 is 40, as 40 is the smallest number that both 5 and 8 can divide into without a remainder.
What is the LCM of 3, 4, and 5?
The LCM of 3, 4, and 5 is 60, as 60 is the smallest common multiple shared by these numbers.
What is the LCD of 7 and 8?
The least common denominator (LCD) of 7 and 8, similar to the LCM, is 56, which is the smallest number both can divide into.
What is the LCM of 9 and 4?
The LCM of 9 and 4 is 36, as 36 is the smallest number that is a multiple of both 9 and 4.
How to find the LCM of fractions?
To find the LCM of fractions, first find the LCM of the denominators, which will serve as the common denominator for the fractions.
What is the LCM of 24 and 5?
The LCM of 24 and 5 is 120, as 120 is the smallest number that both 24 and 5 can divide into without leaving a remainder.

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