Least Common Multiple (LCM) of 113 and 84
The least common multiple (LCM) of 113 and 84 is 9492.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 113 and 84?
First, calculate the GCD of 113 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 84 = 1 remainder 29 |
| 2 | 84 ÷ 29 = 2 remainder 26 |
| 3 | 29 ÷ 26 = 1 remainder 3 |
| 4 | 26 ÷ 3 = 8 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 115 | 3105 |
| 99 and 167 | 16533 |
| 168 and 109 | 18312 |
| 60 and 151 | 9060 |
| 125 and 148 | 18500 |