Least Common Multiple (LCM) of 35 and 194
The least common multiple (LCM) of 35 and 194 is 6790.
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 35 and 194?
First, calculate the GCD of 35 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 194 = 0 remainder 35 |
| 2 | 194 ÷ 35 = 5 remainder 19 |
| 3 | 35 ÷ 19 = 1 remainder 16 |
| 4 | 19 ÷ 16 = 1 remainder 3 |
| 5 | 16 ÷ 3 = 5 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 12 | 96 |
| 66 and 123 | 2706 |
| 93 and 25 | 2325 |
| 119 and 109 | 12971 |
| 50 and 74 | 1850 |