Least Common Multiple (LCM) of 109 and 72
The least common multiple (LCM) of 109 and 72 is 7848.
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 72?
First, calculate the GCD of 109 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 72 = 1 remainder 37 |
| 2 | 72 ÷ 37 = 1 remainder 35 |
| 3 | 37 ÷ 35 = 1 remainder 2 |
| 4 | 35 ÷ 2 = 17 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 58 | 5336 |
| 125 and 27 | 3375 |
| 195 and 169 | 2535 |
| 126 and 14 | 126 |
| 44 and 195 | 8580 |