Least Common Multiple (LCM) of 109 and 102
The least common multiple (LCM) of 109 and 102 is 11118.
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 102?
First, calculate the GCD of 109 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 102 = 1 remainder 7 |
| 2 | 102 ÷ 7 = 14 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 84 | 1680 |
| 75 and 161 | 12075 |
| 54 and 37 | 1998 |
| 137 and 96 | 13152 |
| 44 and 23 | 1012 |