Least Common Multiple (LCM) of 84 and 113
The least common multiple (LCM) of 84 and 113 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 84 and 113?
First, calculate the GCD of 84 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 113 = 0 remainder 84 |
| 2 | 113 ÷ 84 = 1 remainder 29 |
| 3 | 84 ÷ 29 = 2 remainder 26 |
| 4 | 29 ÷ 26 = 1 remainder 3 |
| 5 | 26 ÷ 3 = 8 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 89 | 7209 |
| 188 and 45 | 8460 |
| 121 and 141 | 17061 |
| 103 and 84 | 8652 |
| 46 and 197 | 9062 |