Least Common Multiple (LCM) of 194 and 72
The least common multiple (LCM) of 194 and 72 is 6984.
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 194 and 72?
First, calculate the GCD of 194 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 72 = 2 remainder 50 |
| 2 | 72 ÷ 50 = 1 remainder 22 |
| 3 | 50 ÷ 22 = 2 remainder 6 |
| 4 | 22 ÷ 6 = 3 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 53 | 6148 |
| 181 and 127 | 22987 |
| 123 and 196 | 24108 |
| 118 and 118 | 118 |
| 125 and 156 | 19500 |