The Least Common Multiple Of 12 And 5

Ex 3.7, 10 Find LCM of (a) 9 and 4 (b) 12 and 5 (c) 6 5 (d) 15 4 from www.teachoo.com

Introduction

Finding the least common multiple (LCM) is a common problem in arithmetic. It is particularly useful in situations where we need to find a common denominator for fractions with different denominators. In this article, we will focus on finding the LCM of 12 and 5. We will explain what LCM is and how to find it step by step.

What is LCM?

LCM is the smallest positive integer that is a multiple of two or more numbers. In other words, it is the smallest number that is divisible by both 12 and 5 without leaving a remainder. LCM is also sometimes called the lowest common multiple.

Method 1: Prime Factorization

One way to find the LCM of 12 and 5 is by using the prime factorization method. To do this, we need to find the prime factors of both numbers. Prime factors are the prime numbers that can divide a number without leaving a remainder. The prime factorization of 12 is 2 x 2 x 3. The prime factorization of 5 is 5. To find the LCM, we need to take the highest power of each prime factor. In this case, the highest power of 2 is 2 x 2 = 4, and the highest power of 3 is 3. The highest power of 5 is simply 5. Therefore, the LCM of 12 and 5 is 4 x 3 x 5 = 60.

Method 2: Listing Multiples

Another way to find the LCM of 12 and 5 is by listing their multiples. Multiples are the numbers that can be divided by a given number without leaving a remainder. We can list the multiples of 12 and 5 until we find the smallest number that is divisible by both. The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ... The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ... The smallest number that appears in both lists is 60. Therefore, the LCM of 12 and 5 is 60.

Method 3: Using Division

A third way to find the LCM of 12 and 5 is by using division. We can divide multiples of one number by the other number until we find a multiple that is divisible by both. Let's start by dividing multiples of 12 by 5. 12 ÷ 5 = 2 remainder 2. 24 ÷ 5 = 4 remainder 4. 36 ÷ 5 = 7 remainder 1. 48 ÷ 5 = 9 remainder 3. 60 ÷ 5 = 12 remainder 0. Therefore, the smallest multiple of 12 that is divisible by 5 is 60. Now, let's divide multiples of 5 by 12. 5 ÷ 12 = 0 remainder 5. 10 ÷ 12 = 0 remainder 10. 15 ÷ 12 = 1 remainder 3. 20 ÷ 12 = 1 remainder 8. 25 ÷ 12 = 2 remainder 1. 30 ÷ 12 = 2 remainder 6. 35 ÷ 12 = 2 remainder 11. 40 ÷ 12 = 3 remainder 4. 45 ÷ 12 = 3 remainder 9. 50 ÷ 12 = 4 remainder 2. 55 ÷ 12 = 4 remainder 7. 60 ÷ 12 = 5 remainder 0. Therefore, the smallest multiple of 5 that is divisible by 12 is also 60.

Conclusion

In conclusion, there are several ways to find the LCM of 12 and 5. We can use the prime factorization method, listing multiples, or division. Regardless of the method, we arrive at the same answer: the LCM of 12 and 5 is 60. LCM is a useful concept in arithmetic that helps us simplify fractions and solve various problems.