Least Common Multiple (LCM) of 109 and 100
The least common multiple (LCM) of 109 and 100 is 10900.
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 100?
First, calculate the GCD of 109 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 100 = 1 remainder 9 |
| 2 | 100 ÷ 9 = 11 remainder 1 |
| 3 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 86 | 258 |
| 103 and 176 | 18128 |
| 119 and 40 | 4760 |
| 107 and 73 | 7811 |
| 120 and 140 | 840 |