The Lcm Of 12 And 16 Explained

LCM of 12 and 16 How to Find LCM of 12, 16? from www.cuemath.com

What is LCM?

LCM stands for Least Common Multiple, which is the smallest number that is a multiple of two or more given numbers. In other words, it is the lowest common denominator of two or more numbers.

How to Find the LCM of 12 and 16

To find the LCM of 12 and 16, we need to first list down the multiples of both numbers. We can start by listing the multiples of 12 and 16 separately. Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432, 444, 456, 468, 480, 492, 504, 516, 528, 540, 552, 564, 576, 588, 600, 612, 624, 636, 648, 660, 672, 684, 696, 708, 720, 732, 744, 756, 768, 780, 792, 804, 816, 828, 840, 852, 864, 876, 888, 900, 912, 924, 936, 948, 960 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

Method 1: Listing Multiples

We can find the LCM of 12 and 16 by looking for the smallest number that appears in both lists. In this case, we can see that 48 is the smallest number that appears in both lists, so the LCM of 12 and 16 is 48.

Method 2: Prime Factorization

Another method to find the LCM of 12 and 16 is by using prime factorization. We can break down both numbers into their prime factors and then find the product of the highest powers of each prime factor. Prime factors of 12: 2 x 2 x 3 Prime factors of 16: 2 x 2 x 2 x 2 To find the LCM, we need to take the highest power of each prime factor: 2 x 2 x 2 x 2 x 3 = 48.

Why is LCM Important?

LCM is important in many mathematical operations such as adding and subtracting fractions with different denominators. In order to add or subtract fractions, we need to find their common denominator, which is the LCM of their denominators.

Conclusion

In summary, the LCM of 12 and 16 is 48. We can find the LCM by listing down the multiples of both numbers and looking for the smallest number that appears in both lists, or by using prime factorization to find the product of the highest powers of each prime factor. LCM is an important concept in mathematics and is particularly useful in operations involving fractions.