Least Common Multiple (LCM) of 109 and 84
The least common multiple (LCM) of 109 and 84 is 9156.
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 109 and 84?
First, calculate the GCD of 109 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 84 = 1 remainder 25 |
| 2 | 84 ÷ 25 = 3 remainder 9 |
| 3 | 25 ÷ 9 = 2 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 72 | 3384 |
| 161 and 92 | 644 |
| 183 and 67 | 12261 |
| 151 and 135 | 20385 |
| 56 and 160 | 1120 |