Explanation And Solution For Lcm Of 7 And 12

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What is LCM?

LCM stands for Least Common Multiple. It is the smallest multiple that two or more numbers have in common. In simple terms, it is the smallest number that is a multiple of both given numbers. For example, the LCM of 3 and 5 is 15 because it is the smallest multiple of both 3 and 5.

How to find LCM?

To find the LCM of two numbers, we need to find the multiples of each number until we find the smallest multiple that is common to both numbers. For example, let's find the LCM of 7 and 12. Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210 Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240 From the above multiples, we can see that the LCM of 7 and 12 is 84 because it is the smallest multiple that is common to both numbers.

Formula for finding LCM

There is also another method to find the LCM using a formula. The formula is LCM = (a*b)/gcd(a,b), where a and b are the given numbers and gcd(a,b) is the greatest common divisor of a and b. In our example, a=7 and b=12. The greatest common divisor of 7 and 12 is 1. Therefore, the LCM of 7 and 12 is (7*12)/1 = 84.

Why is LCM important?

LCM is important in many mathematical calculations, especially in fractions. It is used to add, subtract, multiply and divide fractions. To perform these operations, we need to find the LCM of the denominators of the fractions. For example, to add 1/3 and 2/5, we need to find the LCM of 3 and 5, which is 15. Then, we convert the fractions to have a common denominator of 15 and add the numerators. The result is (1*5 + 2*3)/15 = 11/15.

Conclusion

In conclusion, LCM is an important concept in mathematics, and it is used in many calculations. To find the LCM of two numbers, we can either list the multiples or use the formula. In our example, the LCM of 7 and 12 is 84.