Understanding Lcm Of 9 And 16

LCM of 9 and 16 How to Find LCM of 9, 16? from www.cuemath.com

What is LCM?

LCM or Least Common Multiple is the smallest number that is a multiple of two or more given numbers. In simpler terms, LCM is the smallest number that is a multiple of all the given numbers.

How to find the LCM of 9 and 16?

To find the LCM of 9 and 16, we need to find the multiples of both numbers and find the smallest number that is common in both lists. Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, 459, 468, 477, 486, 495, 504, 513, 522, 531, 540, 549, 558, 567, 576, 585, 594, 603, 612, 621, 630, 639, 648, 657, 666, 675, 684, 693, 702, 711, 720, 729, 738, 747, 756, 765, 774, 783, 792, 801, 810, 819, 828, 837, 846, 855, 864, 873, 882, 891, 900 Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320, 336, 352, 368, 384, 400, 416, 432, 448, 464, 480, 496, 512, 528, 544, 560, 576, 592, 608, 624, 640, 656, 672, 688, 704, 720, 736, 752, 768, 784, 800, 816, 832, 848, 864, 880, 896, 912, 928, 944, 960, 976, 992, 1008, 1024, 1040, 1056, 1072, 1088, 1104, 1120, 1136, 1152, 1168, 1184, 1200, 1216, 1232, 1248, 1264, 1280, 1296, 1312, 1328, 1344, 1360, 1376, 1392, 1408, 1424, 1440, 1456, 1472, 1488, 1504, 1520, 1536 From the above lists, we can see that the smallest number common in both lists is 144. Hence, the LCM of 9 and 16 is 144.

Why is LCM important?

LCM is an important concept in mathematics as it is used in various real-life situations like calculating time, distance, and many more. For example, if two trains start from a station at the same time, we can use LCM to find the time at which they will meet.

Formula to find LCM

There is a formula to find the LCM of two given numbers. Let's say we need to find the LCM of two numbers 'a' and 'b'. Then, LCM(a,b) = (a * b) / GCD(a,b) Here, GCD is the Greatest Common Divisor of the two numbers.

How to find GCD?

To find the GCD of two numbers, we need to find the highest common factor of both numbers. The most common method to find the GCD is by using the Euclidean algorithm. For example, to find the GCD of 9 and 16: Step 1: Divide the larger number by the smaller number and find the remainder. 16 / 9 = 1 remainder 7 Step 2: Divide the smaller number by the remainder obtained in step 1 and find the remainder. 9 / 7 = 1 remainder 2 Step 3: Repeat step 2 until the remainder is 0. 7 / 2 = 3 remainder 1 2 / 1 = 2 remainder 0 Step 4: The GCD is the remainder obtained in the last step before 0. Hence, the GCD of 9 and 16 is 1.

Conclusion

In conclusion, LCM is the smallest number that is a multiple of two or more given numbers. To find the LCM of 9 and 16, we need to find the smallest number common in the list of multiples of both numbers, which is 144. LCM is an important concept in mathematics and is used in various real-life situations. There is a formula to find the LCM of two numbers, and to find the GCD, we can use the Euclidean algorithm.