Least Common Multiple (LCM) of 68 and 196
The least common multiple (LCM) of 68 and 196 is 3332.
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 68 and 196?
First, calculate the GCD of 68 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 196 = 0 remainder 68 |
| 2 | 196 ÷ 68 = 2 remainder 60 |
| 3 | 68 ÷ 60 = 1 remainder 8 |
| 4 | 60 ÷ 8 = 7 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 99 | 9900 |
| 57 and 161 | 9177 |
| 116 and 78 | 4524 |
| 35 and 176 | 6160 |
| 55 and 141 | 7755 |