Least Common Multiple (LCM) of 117 and 100
The least common multiple (LCM) of 117 and 100 is 11700.
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 117 and 100?
First, calculate the GCD of 117 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 100 = 1 remainder 17 |
| 2 | 100 ÷ 17 = 5 remainder 15 |
| 3 | 17 ÷ 15 = 1 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 200 | 19800 |
| 23 and 63 | 1449 |
| 131 and 179 | 23449 |
| 67 and 102 | 6834 |
| 196 and 196 | 196 |