Least Common Multiple (LCM) of 84 and 107
The least common multiple (LCM) of 84 and 107 is 8988.
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 107?
First, calculate the GCD of 84 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 107 = 0 remainder 84 |
| 2 | 107 ÷ 84 = 1 remainder 23 |
| 3 | 84 ÷ 23 = 3 remainder 15 |
| 4 | 23 ÷ 15 = 1 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 137 | 15755 |
| 157 and 77 | 12089 |
| 163 and 84 | 13692 |
| 100 and 120 | 600 |
| 99 and 196 | 19404 |