Least Common Multiple (LCM) of 193 and 72
The least common multiple (LCM) of 193 and 72 is 13896.
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 193 and 72?
First, calculate the GCD of 193 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 72 = 2 remainder 49 |
| 2 | 72 ÷ 49 = 1 remainder 23 |
| 3 | 49 ÷ 23 = 2 remainder 3 |
| 4 | 23 ÷ 3 = 7 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 11 | 1199 |
| 39 and 101 | 3939 |
| 104 and 37 | 3848 |
| 151 and 38 | 5738 |
| 53 and 116 | 6148 |