Least Common Multiple (LCM) of 61 and 194
The least common multiple (LCM) of 61 and 194 is 11834.
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 61 and 194?
First, calculate the GCD of 61 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 194 = 0 remainder 61 |
| 2 | 194 ÷ 61 = 3 remainder 11 |
| 3 | 61 ÷ 11 = 5 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 170 | 4590 |
| 138 and 36 | 828 |
| 65 and 112 | 7280 |
| 38 and 122 | 2318 |
| 140 and 176 | 6160 |