Understanding The Least Common Multiple Of 6 And 14

LCM of 6 and 14 How to Find LCM of 6, 14? from www.cuemath.com

What is the Least Common Multiple?

The Least Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers. In simpler terms, it is the smallest number that two or more given numbers divide into evenly.

Why is the LCM Important?

The LCM is important in many areas of mathematics, including fractions and algebra. In fractions, finding the LCM is necessary for adding and subtracting fractions with different denominators. In algebra, the LCM is used when simplifying expressions and solving equations.

How to Find the LCM of 6 and 14

To find the LCM of 6 and 14, we need to list the multiples of each number and find the smallest multiple they have in common. Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180 Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294, 308, 322, 336, 350, 364, 378, 392, 406, 420 As we can see from the above lists, the smallest multiple that 6 and 14 have in common is 42. Therefore, the LCM of 6 and 14 is 42.

Why is 42 the LCM of 6 and 14?

The LCM of 6 and 14 is 42 because it is the smallest multiple that both 6 and 14 share. In other words, 42 is the smallest number that is divisible by both 6 and 14 without leaving a remainder.

Other Ways to Find the LCM

Another way to find the LCM is by using prime factorization. To do this, we need to find the prime factors of each number and then multiply them together, taking the highest exponent for each factor. Prime factors of 6: 2 x 3 Prime factors of 14: 2 x 7 Multiplying the prime factors together, we get: 2 x 3 x 7 = 42 Therefore, the LCM of 6 and 14 is 42.

Conclusion

In conclusion, the LCM is an important concept in mathematics that is used in many areas. To find the LCM of two or more numbers, we can list their multiples or use prime factorization. In the case of 6 and 14, their LCM is 42, which is the smallest multiple they have in common.