Least Common Multiple (LCM) of 109 and 68
The least common multiple (LCM) of 109 and 68 is 7412.
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 68?
First, calculate the GCD of 109 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 68 = 1 remainder 41 |
| 2 | 68 ÷ 41 = 1 remainder 27 |
| 3 | 41 ÷ 27 = 1 remainder 14 |
| 4 | 27 ÷ 14 = 1 remainder 13 |
| 5 | 14 ÷ 13 = 1 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 94 and 99 | 9306 |
| 168 and 121 | 20328 |
| 195 and 51 | 3315 |
| 114 and 85 | 9690 |
| 150 and 176 | 13200 |