Least Common Multiple (LCM) of 121 and 196
The least common multiple (LCM) of 121 and 196 is 23716.
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 121 and 196?
First, calculate the GCD of 121 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 196 = 0 remainder 121 |
| 2 | 196 ÷ 121 = 1 remainder 75 |
| 3 | 121 ÷ 75 = 1 remainder 46 |
| 4 | 75 ÷ 46 = 1 remainder 29 |
| 5 | 46 ÷ 29 = 1 remainder 17 |
| 6 | 29 ÷ 17 = 1 remainder 12 |
| 7 | 17 ÷ 12 = 1 remainder 5 |
| 8 | 12 ÷ 5 = 2 remainder 2 |
| 9 | 5 ÷ 2 = 2 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 46 | 690 |
| 144 and 117 | 1872 |
| 30 and 36 | 180 |
| 112 and 151 | 16912 |
| 69 and 123 | 2829 |