Least Common Multiple (LCM) of 117 and 196
The least common multiple (LCM) of 117 and 196 is 22932.
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 196?
First, calculate the GCD of 117 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 196 = 0 remainder 117 |
| 2 | 196 ÷ 117 = 1 remainder 79 |
| 3 | 117 ÷ 79 = 1 remainder 38 |
| 4 | 79 ÷ 38 = 2 remainder 3 |
| 5 | 38 ÷ 3 = 12 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 97 | 8730 |
| 110 and 184 | 10120 |
| 79 and 22 | 1738 |
| 153 and 46 | 7038 |
| 84 and 37 | 3108 |